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THE 



ELEMENTS OF LOGIC, 



A TEXT-BOOK 



FOR SCHOOLS AND COLLEGES; 



THE ELEMENTARY LESSONS IN LOGIC. 

BY 

W. STANLEY JEVONS, LL.D., F.R.S., 

LATE PROFESSOR OF LOGIC IN OWENS COLLEGE, MANCHESTER, 



RECAST BY 
DAVID J. HILL, LL.D., 

PRES.^ENT OF THE UNIVERSITY AT LEWISBURG, PA., AND AUTHOR OF HILL'S 
RHETORICAL SERIES. 



No.. 
°P WASHIN ( 



SHELDON AND COMPANY, 

JtEW YORK AND CHICAGO. 



BCiog 
48 

Copy ^» 

PRESIDENT HILL'S TEXT-BOOKS. 



ist. 

THE ELEMENTS OF RHETORIC 
AND COMPOSITION. 

2d. 

THE SCIENCE OF RHETORIC. 

3a. 
THE ELEMENTS OF LOGIC. 



Copyright, 1883, by Sheldon &> Co. 






Elecirotyped by Smith & McDougal, 82 Beekman St., New York. 



* 



•r* m^ ^ j ^ * ^ 



* 



BY THE EDITOR. 



Although there are many elementary works on 
Logic, it has been for a long time felt that there is 
no text-book that precisely meets the wants of our 
colleges and normal schools. The nearest approach to 
the desideratum is the "Elementary Lessons in Logic" 
which constitutes the substance of this book. Its 
merits are its fresh treatment of the subject, its ful- 
ness and felicity of illustration, its clearness and vigor 
of style, its recognition of the logical methods of 
science as a part of Logic, and its comprehensive pre- 
sentation of recent views on the subject of reasoning. 
It was designed by its author, Professor W. Stanley 
Jevons, as a hand-book for students in the English 
Universities. It is this alone that has stood in the 
way of its general adoption as a text-book in this 
country, for the methods of study in England and 
America are essentially different. In England the 
student reads under the direction of a Tutor and thus 
prepares himself for a public examination. In America 
daily recitations on the topical plan are almost univer- 



IV PREFACE. 

sal in the study of this subject. Although Professor* 
Jevons divided his work into Lessons, these bore no 
relation to the amount usually assigned for a daily les- 
son, and so failed to provide that distribution of the 
matter that is desirable for the class-room. It is also a 
defect of this method of dividing a subject that it fails 
to present the logical relations of parts and the organic 
unity of the whole. But the chief defect of the original 
work, as a text-book for classes using the topical 
method, is the want of an exact analysis of the topics 
and a discrimination of that which is essential and 
should be firmly fixed in the memory, from that which 
is merely explanatory and illustrative and needs only to 
be carefully read and comprehended. The amount of 
illustration is superabundant in some cases, and tends 
to distract the mind and render it less attentive to 
great principles than is consistent with a firm grasp of 
such a science. The amount of matter in the book, 
unless a part be subordinated, is too great to be 
mastered in the single term that is usually given to the 
study even in the highest grade of schools in this 
country. 

The publishers have been led to believe from the rep- 
resentations of professors of Logic who have had exten- 
sive experience in teaching the science, that a recasting 
of Professor Jevons" work, with special reference to the 
difficulties enumerated above, would render it in every 
.respect adapted to meet the confessed demand for a 
thorough text-book on this subject. It would have 
been most desirable if Professor Jevons himself might 
have recast the book with these considerations in mind, 
but that was rendered impossible by his sudden death 



PREFACE. V 

by drowning. In attempting to adapt this admirable 
treatise to the needs of American students, I have 
sought to make the following changes : 

1. To introduce a complete and precise Analysis, 
and to distribute the text in such a manner as to 
render the method and arrangement of the book as 
lucid as possible. 

2. To give prominence to cardinal principles and 
important doctrines by stating them in large type, 
while matter that is simplv explanatory and illustrative 
is subordinated by being thrown into smaller type. 

3. To impart to the treatment of Inductive Logic 
more system and co-ordination than are found in the 
original work. 

4. To give unity to the treatment of the subject by 
placing the discussion of Eecent Logical Views at the 
end of the text, instead of near the middle of the book, 
thus avoiding a break in the continuity of the better 
established doctrines of the science. 

5. To facilitate reviews by placing at the end of 
each section a summary of the topics treated of in 
that section. 

6. To impart some information concerning writers 
on Logic named in the text, of whom the average 
student cannot be presumed to have any exact knowl- 
edge. This information is inserted in the Index and 
Glossary under the names of the writers referred to. 

I have for the most part retained the language of the 
author, only adding where addition seemed to be 
necessary to clearness. Such errors and infelicities of 
expression as I have noticed, I have corrected. The 



VI PREFACE. 

singular clearness of Professor Jevons's mind, however, 
has rendered the occurrence of these infrequent. 

Although the opinion of teachers may vary upon this 
point, the plan of requiring a close reproduction of the 
text in largo print, with questioning upon the matter 
in the small type, will probably commend itself in 
practice. In the review the parts in small type might 
be omitted. Questions for examinations are inserted 
at the end of the book. 

In the hope that the work as recast may be found 
useful to teachers and students, this revision is offered 
to the public. 

The Editor. 



A SKETCH 



OP 



THE AUTHOR'S LIFE 



WILLIAM STANLEY JEVONS was born in Liverpool, in 
September, 1835. His father, Thomas Jevons, was an iron mer- 
chant, and his mother was a daughter of William Roscoe, the 
banker and historian. 

Having obtained his early education at the High School of 
Liverpool and at the Mechanics' Institution, at the age of sixteen 
he entered University College, London. There he became so- 
distinguished in mathematics and chemistry that at the age of 
nineteen, while still an undergraduate, he was invited to a posi- 
tion in the Sydney Mint, Australia. He accepted this appoint- 
ment, but after five years' residence in Australia, he returned to 
London, completed his course of study and took the Master's 
degree. He attained the highest honors in Logic, Moral Phil- 
osophy and Political Economy. 

In 1863 Jevons began his work as a teacher in Owens College, 
Manchester, and three years later was elected Professor of the 
three studies in which he especially excelled. After ten years of 
distinguished service at Manchester, during which period he won 
an extended reputation as a writer, Professor Jevons felt the 
burden of his varied duties to be too heavy for him and accepted 



Vlll AUTHOR'S LIFE. 

the chair of Political Economy in University College, London. 
Even the duties of this position, though not extensive, became 
oppressive to him with health that had grown uncertain, and in 
the winter of 1880-1 he retired to private life. 

His life was terminated by an accident on the 13th of August, 
1882, while bathing at Galley Hill, on the Sussex coast. The 
precise cause of his death in the water is not known, but it is 
supposed that in his feeble health he was not able to resist the 
nervous shock caused by the excitement of bathing, and being 
disabled he was drowned. 

As a writer Professor Jevons was remarkably fertile. In 
addition to the present work, he produced on the subject of logic 
three notable books. A work entitled " Pure Logic" was pub- 
lished in 1864. "The Substitution of Similars" (1869) was an 
attempt to simplify all reasoning by referring it to a single 
principle more comprehensive than Aristotle's dicta. "The 
Principles of Science " (1874) was, in effect, the application of 
this principle to the details of scientific method, and an exposition 
of the fundamental postulates on which all human science rests. 
Both works have called forth considerable controversy, but the 
latter in particular has been useful in the direction of scientific 
reasoning. More recently Professor Jevons has reviewed with 
searching criticism the logical work of the late John Stuart Mill. 
Referring to his treatises on Logic and his review of Mill, the 
" Revue Philosophique " says: " His great work ' The Principles 
of Science ' and his recent polemic against the Logic of Stuart 
Mill have given him a distinguished rank among English 
logicians." The same notice also adds that "the elementary 
works of Stanley Jevons have become classic." 

We cannot properly close this sketch without a brief reference 
to Professor Jevons' works on Political Economy, to which he 
devoted many of his best years. The most popular of these are 



AUTHOR'S LIFE. IX 

The " Theory of Political Economy " (1871), an attempt to present 
the subject under a mathematical form ; " Money and the Mech- 
anism of Exchange " (1875), a more popular presentation of the 
subject, being a contribution to the International Scientific 
Series ; and " The Primer of Political Economy " (1878), a greatly 
simplified introduction to the subject. A more special and 
technical production is the work on " The Coal Question." 

" As a man," says the Editor of the English periodical Mind, 
" Jevons was most lovable. Of a shy and retiring disposi- 
tion, he never mixed much in general society, but he had a 
geniality of nature and sweetness of temper, with a ready help- 
fulness, which secured him an inner circle of most devoted 
friends. With so firm a grasp as he had of his own convictions 
and opinions, he was admirable for the spirit in which he courted 
and welcomed criticism." 

In recognition of his attainments Professor Jevons was made 
a Fellow of the Royal Society, and the honorary degree of 
Doctor of Laws was conferred upon him by the University 
of Edinburgh. The highest authorities in Europe accord to him 
"an assured reputation as an original thinker and writer in the 
two departments of Logic and Political Economy." 

The Editor. 




N&LYSIS 

INTRODUCTION. 



PAGE 

1. Definition op Logic 1 

2. Nature op a Law op Thought 2 

3. A Science op Thought Possible 3 

4. Distinction between Form and Matter . . * 5 

5. Logic a General Science 6 

6. The Particular Sciences, Special Logics 6 

7. Logic both a Science and an Art 7 

8. The Usefulness of Logic 8 

9. Analysis of an Argument 9 

10. Theories of the Real Subject-matter of Logic 10 

11. The Three Logical Operations of Mind 12 

12. Method of Treatment 16 



CHAPTER I 
TERMS. 

SECTION I.— THE VARIOUS KINDS OF TERMS. 

1. The Meaning of " Term" Explained 17 

2. Categorematic and Syncategorematic Words 18 

3. Singular Terms 20 

4. General Terms 20 

5. Collective Terms 21 

6. Concrete and Abstract Terms 22 



Xll ANALYSIS. 

PAGE 

7. Positive and Negative Terms 24 

8. Privative Terms 26 

9. Relative and Absolute Terms 27 

10. Summary 28 

SECTION II.— THE AMBIGUITY OF TERMS. 

1. Importance op Avoiding Ambiguity 30 

2. Univocal and Equivocal Terms 31 

3. Kinds and Causes of Ambiguity 33 

SECTION III.— EXTENSION AND INTENSION. 

1. Importance op Understanding this Double Mean- 

ing 39 

2. Meaning op Extension and Intension 39 

3. Various Forms op Expressing Extension and Inten- 

sion 41 

4. The Variation of Extension and Intension 42 

5. The Law of Variation 42 

6. connotative and non-connotative terms 43 

SECTION IV.-THE GROWTH OF LANGUAGE. 

1. The Two Principal Processes of Growth 46 

2. Generalization 47 

3. Specialization 50 

4. desynon ymization 51 

5. Metaphorical Extension of Meaning 52 

6. Origin of the Mental Vocabulary. 53 

7. The Fertility of Root words 54 

SECTION V.— THE PERFECT AND THE IMPERFECT 
KNOWLEDGE OF TERMS. 

1. Statement of the Question 56 

2. Scheme of Distinctions 56 

3. The Intuitive and Symbolic Methods Compared 62 



ANALYSIS. Xlll 

CHAPTEE II. 
PROPOSITIONS. 

SECTION I.— THE KINDS OF PROPOSITIONS. 

PAGE 

1. Meaning of " Pkoposition " Explained. . . 64 

2. Analysis op a Proposition 65 

3. Categorical and Conditional Propositions 66 

4. The Quantity and Quality op Propositions 67 

5. Aristotle's View of Quantity 68 

6. Names of the Four Propositions 70 

7. Variations from the Logical Form 71 

8. The Modality of Propositions 73 

SECTION II.— THE OPPOSITION OF PROPOSITIONS. 

1. The Four Propositions Explained 75 

2. The Distribution of Terms 79 

3. Table of Results 80 

4. Relations of the Four Propositions 80 

5. The Scheme of Opposition 83 

6. The Laws of Opposition 83 

7. The Conditions of Opposition . . 84 

8. The Matter of Propositions 85 



SECTION III.— CONVERSION AND IMMEDIATE 
INFERENCE. 

1. The Nature of Inference 86 

2. Conversion of Propositions 87 

3. Immediate Inference 90 



XIV ANALYSIS. 



SECTION IV.— THE LOGICAL ANALYSIS OF SEN- 
TENCES. 

PAGE 

1. Relation of Logic to this Topic 93 

2. The Grammatical and the Logical Predicate 94 

3 The Plurality op Propositions in a Sentence 95 

4. Complex Sentences 96 

5. Modes op Exhibiting Construction 99 



CHAPTER III. 
SYLLOGISMS. 

SECTION I— THE LAWS OF THOUGHT. 
f 

1. The Statement of the Primary Laws of Thought . 104 

2. Explanation of the Laws 105 

3. The Canons of Syllogism 108 

4. The Axioms of Mathematics 110 

5. Aristotle's Dicta Ill 

SECTION II.— THE RULES OF THE SYLLOGISM. 

1. The Definition of " Syllogism " 113 

2. The Meaning op " Middle Term " . 114 

3. The Use of Middle Term in Syllogism 114 

4. Statement of the Rules of Syllogism 115 

5. Explanation of the Rules 116 

SECTION III.— THE MOODS AND FIGURES OF 
THE SYLLOGISM. 

1. Explanation op " Moods " 124 

2. The Number of Valid Moods 125 

3. Explanation op " Figures " 127 



ANALYSIS. XV 

PAGE 

4. The Valid Moods in the Different Figures 128 

5. Conclusions Proved in the Different Figures 130 

SECTION IV.— THE REDUCTION OF SYLLOGISMS. 

1. The Mnemonic Verses 133 

2. Explanation of the Mnemonic Verses 134 

3. Conclusions from Particular Premises 139 

SECTION V.— IRREGULAR AND COMPOUND 
SYLLOGISMS. 

1. The Irregular Mode of Expressing Inferences 141 

2. Explanation of " Enthymeme " 142 

3. Prosyllogisms and Episyllogisms 144 

4 Sorites 145 

5. Syllogisms in Extension and in Intension 148 

SECTION VI.— CONDITIONAL SYLLOGISMS. 

1. Classification of Propositions 149 

2. Antecedent and Consequent 150 

3. Kinds of Hypothetical Syllogisms 151 

4 The Rule for Hypothetical Syllogisms 152 

5. The Reduction of Hypothetical to Categorical 

Syllogisms 153 

6. Fallacies in Hypothetical Syllogisms 155 

7. Disjunctive Syllogisms 156 

8. The Dilemma 158 



CHAPTER IY. 
FALLACIES. 

SECTION I.— LOGICAL FALLACIES. 

1. Classification of Logical Fallacies 162 

2. The Fallacy of Equivocation 163 

3. The Fallacy of Amphibology 164 



XVI ANALYSIS. 

PAGE 

4. The Fallacy op Composition 165 

5. The Fallacy of Division 166 

6. The Fallacy op Accident 167 

7. The Fallacy op the Figure op Speech • , . 168 

SECTION II.— MATERIAL FALLACIES. 

1. The Classification of Material Fallacies 169 

2. The Fallacy of Accident and its Converse 169 

3. The Fallacy of Irrelevant Conclusion 171 

4. The Fallacy of Petitio Principii 173 

5. The Fallacy of the Consequent 175 

6. The Fallacy of False Cause 175 

7. The Fallacy of Many Questions 176 



CHAPTEK V. 
INDUCTION. 

SECTION I.— THE INDUCTIVE SYLLOGISM. 

1. Induction and Deduction Contrasted 178 

2. Explanation of Traduction 179 

3. Importance of Induction 180 

4. Perfect and Imperfect Induction 181 

5. The Difference between Perfect and Imperfect 

Induction 181 

6. The Perfect Inductive Syllogism 183 

7. The Perfect Inductive Syllogism Disjunctive 184 

8. The Imperfect Inductive Syllogism 184 

9. The Fundamental Assumption op Induction 185 

SECTION II.— THE FORMS OF INDUCTION. 

1. The Character of the Data 187 

2, Special Kinds of Induction 195 



Ill 
ANALYSIS. XVii 



CHAPTEE VI. 
METHOD. 

SECTION I.— INDUCTIVE METHOD. 

PAGE 

1. The Search for Facts 201 

2. The Rule for Observation. .' 206 

3. The Uses of Hypothesis and Theory 208 

4. Definitions of Terms Employed in Investigation. . . 212 

5. Canons of Induction 215 

SECTION II.— DEDUCTIVE METHOD. 

1. The Predicables 227 

2. Logical Divisions 234 

3. Dichotomy, or Exhaustive Division 236 

4. Definition 238 

5. Classification 240 

6. Requisites of a Good Classification 242 

7. Denomination 245 

SECTION III.— COMPLETE METHOD. 

1. Empirical and Rational Knowledge 249 

2. The Elements of Complete Method 251 

3. The Nature of Explanation 254 

4. Pascal on Method 257 

5. Descartes on Method 263 

CHAPTEE VII. 
RECENT LOGICAL VIEWS. 

SECTION I.— THE QUANTIFICATION OF THE PREDICATE. 

1. Meaning of the Expression 263 

2. Conversion with a Quantified Predicate 264 



XV111 . ANALYSIS. 

PAGE 

3. The Rule for Conversion 266 

4 Number of Propositions with a Quantified Predi- 
cate 266 

5. Number of Syllogisms with Quantified Predicate. 268 

6. Hamilton's Notation 268 

7. Hamilton's Canon of the Syllogism 270 

SECTION II.— BOOLE'S SYSTEM OF LOGIC. 

1. The Difficulty of Dr. Boole's Statement ... 272 

2. Application of the Law of Excluded Middle 273 

3. Application of the Law of Contradiction 274 

4. Universality of the Method 275 

5. Comparative Excellence of the System 277 

6. The Logical Abacus and the Logical Machine 280 

Questions and Exercises 283 

Index and Glossary 314 




1. Definition of Logic. 

Logic may be most briefly defined as the Science of 
Reasoning. It is more commonly defined, however, as 
the Science of the Laws of Thought, and some lo- 
gicians think it desirable to specify still more accurately 
that it is the Science of the Formal, or of the Necessary 
Laws of Thought. Before these definitions can be of 
any real use to us we must come to a clear understand- 
ing as to the meaning of the expressions ; and it will 
probably appear that there is no great difference be- 
tween them. 



The name of logic is derived from the common Greek word 
Tioyog, which usually means word, or the sign and outward mani- 
festation of any inward thought. But the same word was also 
used to denote the inward thought or reasoning of which words 
are the expression, and it is thus, probably, that later Greek 
writers on reasoning, were led to call their science imaTTJfiTj 
?i,oyiK7j, or logical science ; also texvt] "koyLK-q, or logical art. The 
adjective loyturi, being used alone, soon came to be the name of 
the science, just as Mathematic, Rhetoric, and other names 
ending in"ic" were originally adjectives, but have been con- 
verted into substantives. 



INTRODUCTION. 



2. Nature of a Law of Thought. 

By a Law of Thought we mean a certain uniformity 
or agreement which exists and must exist in the modes 
in which all persons think and reason, so long as they 
do not make what we call mistakes, or fall into self- 
contradiction and fallacy. The laws of thought are 
natural laws with which we have no power to interfere, 
and which are, of course, not to be in any way confused 
with the artificial laws of a country, which are invented 
by men and can be altered by them. Every science is 
occupied in detecting and describing the natural laws 
which are inflexibly observed by the objects treated in 
the science. 

The science of astronomy investigates the uniform or similar 
way in which the heavenly bodies, and, in fact, all material sub- 
stances, tend to fall towards each other, as a stone falls towards 
the earth, or to move round each other under the influence of 
this tendency. The universal law of gravitation is thus the 
natural law of uniformity treated in physical astronomy. 

In chemistry the law of equivalent proportions describes the 
well ascertained fact that each chemical substance enters into 
combination with every other chemical substance only in certain 
definite proportions ; as when exactly eight parts by weight of 
oxygen unite with one part of hydrogen to form water, or 
sixteen parts of oxygen and six parts of carbon unite to form 
carbonic acid in the ordinary burning of a flame or fire. 
Whenever we can detect uniformities, op similarities, we so 
far create science and arrive at natural laws. But there may 
be and are, many things so fickle, complicated, and uncertain, 
that we can never be sure we have detected laws that they will 
uniformly obey ; in such cases no science, in the proper sense of 
the word, is possible. There is no such thing, for instance, as a 
real science of human character, because the human mind is too 
variable and complicated a subject of investigation. There are 



INTRODUCTION. 3 

no two persons so much alike that you may be sure of one acting 
in all circumstances as the other would ; it thus becomes impossi- 
ble to arrange persons in classes so that all who are in the same 
class shall act uniformly in the same manner in any given cir- 
cumstances. 



3. A Science of Thought Possible. 

There is a science of human reason, or thought, apart 
from the many other acts of mind which belong to human 
character, because there are modes in which all persons 
do uniformly think and reason, and must think and 
reason. Thus, if two things are identical with a third 
common thing, they are identical with each other. 
This is a law of thought of a very simple and obvious 
character, and we may observe concerning it : — 

(1) That all people think in accordance with it, 
and agree that they do so as soon as they understand its 
meaning. 

(2) That they think in accordance with it whatever 
may be the subject about which they are thinking. 

Thus, if the things considered are — 

London, 

The Metropolis, 

The most populous city in Great Britain, 

since " the Metropolis is identical with London," and " London 
is identical with the most populous city in Great Britain," it 
follows, necessarily, in all minds, that " the Metropolis is identi- 
cal with the most populous city in Great Britain." 
Again, if we compare the three following things — 

Iron, 

The most useful metal, 

The cheapest metal, — 

and it be allowed that "The most useful metal is Iron," and 



4 INTRODUCTION. 

"Iron is the cheapest metal," it follows, necessarily, in all 
minds, that " the most useful metal is the cheapest." We here 
have two examples of the general truth, that things identical 
with the same thing are identical with each other; and this, we 
may say, is a general or necessary form of thought and reasoning. 
Compare, again, the following three things:— 

The earth, 

Planets, 

Bodies revolving in elliptic orbits. 

We cannot say, as before, that "the earth is identical with the 
planets ; " it is identical only with one of the planets, and we 
therefore say that "it is a planet." Similarly we may say that 
" the planets are bodies revolving in elliptic orbits," but only a 
part of the whole number so revolving. Nevertheless, it follows 
that if the earth is among the planets, and the planets among 
bodies revolving in elliptic orbits, then the earth is among the 
latter. 

A very elementary knowledge of chemistry enables us to 
argue similarly concerning the following : — 

Iron, 

Metals, 

Elementary substances. 

Iron is one of the metals, and metals are elements «or simple 
undecomposable substances, in the sense of being among them 
or a part of them, but not as composing the whole. It follows, 
necessarily, that "Iron is one of the elementary substances." 
We have had, then, two examples of a fixed and necessary form 
of thought, which is necessary and true, whatever the things 
may be to which it is applied. The form of argument may be 
expressed in several different ways, and we shall have to con- 
sider it minutely in the lessons on the syllogism. We may 
express it, for instance, by saying that ' ' part of a part is part 
of the whole." Iron is part of the class of metals, which is part 
of the class of elements— hence iron is part of the class of 
elements. 



INTRODUCTION. 



4. Distinction between Form and Matter. 

In order to apprehend the meaning of the expression, 
" the necessary forms of thought," we must distinguish 
between form and matter. A form is something which 
may remain uniform and unaltered, while the matter 
thrown into that form may be varied. Medals struck 
from the same dies have exactly the same form, but 
they may be of various matter, as bronze, copper, gold, 
or silver. A building of exactly the same form might 
be constructed either of stone or bricks ; furniture of 
exactly similar shape may be made of oak, mahogany, 
walnut wood, etc. Just as we thus familiarly recognize 
the difference of form and substance in common tangi- 
ble things, so we may observe in Logic, that the form 
of an argument is one thing, quite distinct from the 
various subjects or matter which may be treated in that 
form. 

We may almost exhibit to the eye the form of reasoning to 
which belong our two latter arguments, as follows ; — 

(Y) 



(X)....is....(Z) 

If within the three pairs of brackets, marked respectively X, 
r"and Z, we place three names, such that the one in place of X 
may be said to come under that in T, and that in Y under that 
in Z, then it necessarily follows that the first (X) comes under 
the last (Z). 



INTRODUCTION. 



5. Logic a General Science. 

Logic, then, is the science occupied in ascertaining 
and describing all the general forms of thought which 
we must employ so long as we reason validly. These 
forms are very numerous, although the principles on 
which they are constructed are few and simple. It will 
hence appear that logic is the most general of all the 
sciences. Its aid must be more often required than the 
aid of any other science, because all the particular 
sciences treat portions only of existing things, and 
create very different and often unconnected branches of 
knowledge. But logic treats of those principles and 
forms of thought which must be employed in every 
branch of knowledge. It treats of the very origin and 
foundations of knowledge itself ; and though *it is true 
that the logical method employed in one science may 
differ somew r hat from that employed in another science, 
yet, whatever the particular form may be, it must be 
logical, and must conform to the laws of thought. 
There is, in short, something in which all sciences must 
be similar ; to which they must conform so long as they 
maintain what is true and self-consistent; and the 
work of logic is to explain this common basis of all 
science. 

6. The Particular Sciences, Special Logics. 

One name which has been given to Logic, namely, 
the Science of Sciences, very aptly describes the all 
extensive power of logical principles. The cultivators 
of special branches of knowledge appear to have been 
fully aware of the allegiance they owe to the highest of 



INTRODUCTION-. 7 

the sciences, for they have usually given names imply- 
ing this allegiance. The very name of logic occurs as 
part of nearly all the names recently adopted for the 
sciences, which are often vulgarly called the "ologies," 
but are really the " logics," the "o" being only a con- 
necting vowel or part of the previous word. Thus, 
geology is logic applied to explain the formation of the 
earth's crust ; biology is logic applied to the phenomena 
of life ; psychology is logic applied to the nature of the 
mind ; and the same is the case with physiology, ento- 
mology, zoology, teratology, morphology, anthropology, 
theology, ecclesiology, thalattology, and the rest.* Each 
science is thus distinctly confessed to be a special logic. 

7. Logic both a Science and an Art. 

Much discussion of a somewhat trifling character has 
arisen upon the question whether Logic should be con- 
sidered a science only, an art only, op both at the 
same time. Sir W. Hamilton has even taken the 
trouble to classify almost all the writers on logic ac- 
cording as they held one opinion or the other. But it 
seems substantially correct and sufficient to say, that 
logic is a science in so far as it merely investigates the 
necessary principles and forms of thought, and thus 
teaches us to understand in what correct thinking con- 
sists ; but that it becomes an art when it is occupied in 
framing rules to assist persons in detecting false reason- 
ing. 



* Except Philology, which is differently formed, and means the love or 
study of words ; the name of this science, if formed upon the same plan, 
would be logology. 



8 INTRODUCTION. 

A science teaches us to know and an art to do, and all the 

more perfect sciences lead to the creation of corresponding useful 
arts. Astronomy is the foundation of the art of navigation on the 
ocean, as well as of the arrangement of the calendar and chronol- 
ogy. Physiology is the basis of the art of medicine, and chemistry 
is the basis of many useful arts. Logic has similarly been con- 
sidered as the basis of an art of correct reasoning or investigation 
which should teach the true method to be observed in all 
sciences. The celebrated British logician, Duns Scotus, who 
lived in the 13th century, and called logic the Science of 
Sciences, called it also the Art of Arts, expressing fully its 
pre-eminence. Others have thus defined it — " Logic is the art 
of directing the reason aright in acquiring the knowledge of 
things, for the instruction both of ourselves and others." Dr. 
Isaac Watts, adopting this view of logic, called his well-known 
work " The Art of Thinking." 

It may be fairly said, however, that Logic has more the form 
of a science than of an art, for this reason — all persons 
necessarily acquire the faculty and habit of reasoning long before 
they even know the name of logic. This they do by the natural 
exertion of the powers of mind, or by constant but unconscious 
imitation of others. They thus observe correctly, but uncon- 
sciously, the principles of the science in all very simple cases. 
But the contradictory opinions and absurd fallacies which are 
put forth by uneducated persons show that this unaided exercise 
of mind is not to be trusted when the subject of discussion 
presents any difficulty or complexity. 

8. The Usefulness of Logic. 

The study of logic, then, cannot be useless. It not 
only explains the principles on which every one has 
often reasoned correctly before, but points out the 
dangers which exist of erroneous argument. The 
reasoner thus becomes consciously a correct reasoner 
and learns consciously to avoid the snares of fallacy. 
To say that men can reason well without logical science 



INTRODUCTION. 9 

is about as true as to say that they can live healthily 
without medicine. So they can — as long as they are 
healthy ; and so can reasoners do without the science of 
reasoning — as long as they do reason correctly ; but how 
many are there that can do so ? As well might a man 
claim to be immortal in his body as infallible in his 
mind. 

And if it be requisite to say a few words in defence 
of Logic as an art, because circumstances in the past 
history of the science have given rise to misapprehen- 
sion, can it be necessary to say anything in its praise 
as a science? Whatever there is that is great in science 
or in art or in literature, it is the work of intellect. In 
bodily form man is kindred with the brutes, and in his 
perishable part he is but matter. It is the possession of 
conscious intellect, the power of reasoning by general 
notions, that raises him above all else upon the earth ; 
and who can say that the nature and procedure of this 
intellect is not almost the highest and most interesting 
subject of study in which we can engage ? In vain 
would any one deny the truth of the favorite aphorism 
of Sir W. Hamilton — 

In the world there is nothing great but man. 
In man there is nothing great but mind. 

9. Analysis of an Argument. 

It has been explained that Logic is the Science of 
Reasoning, or the Science of those Necessary Laws of 
Thought which must be observed if we are to argue 
consistently with ourselves and avoid self-contradiction. 
Argument or reasoning, therefore, is the strictly proper 



10 INTRODUCTION-. 

subject before us. But the most convenient and usual 
mode of studying logic is to consider first the compo- 
nent parts of which any argument must be made up. 
Just as an architect must be acquainted with the ma- 
terials of a building, or a mechanic with the materials 
of a machine, before he can pretend to be acquainted 
with its construction, so the materials and instruments 
with which we must operate in reasoning are suitably 
described before we proceed to the actual forms of 
argument. 
If we examine a simple argument such as this — 

Iron is a metal, 
Every metal is an element, 
Therefore Iron is an element, — 

we see that it is made up of three statements or asser- 
tions, and that each of these contains, besides minor 
words, two nouns substantive or names of things, and 
the verb " is/' In short, two names, or terms, when 
connected by a verb, make up an assertion or proposi- 
tion ; and three such propositions make up an argument, 
called in this case a syllogism. Hence it is natural and 
convenient first to describe terms, as the simplest parts ; 
next to proceed to the nature and varieties of proposi- 
tions constructed out of them, and then we shall be in 
a position to treat of the syllogism as a whole. Such, 
accordingly, are the three parts of logical doctrine. 

10. Theories of the Real Subject-matter of 
liOgic. 

But though we may say that the three parts of logic 
are concerned with terms, propositions, and syllogisms, 



INTRODUCTION. 11 

it may be said, with equal or greater truth, that the 
acts of mind indicated by those forms of language are 
the real subject of our consideration. The opinions, 
or rather, perhaps, the expressions, of logicians have 
varied on this point. Archbishop Whately says dis- 
tinctly that logic is entirely conversant about language ; 
Sir W. Hamilton, Mr. Manscl, and most other logicians 
treat it as concerned with the acts or states of mind 
indicated by the words ; while Mr. J. S. Mill goes back 
to the things themselves concerning which we argue. 
Is the subject of logic, then, language, thought, or ob- 
jects ? The simplest and truest answer is to say that it 
treats, in a certain sense, of all three. Inasmuch as no 
reasoning process can be explained or communicated to 
another person without words, we are practically limited 
to such reasoning as is reduced to the form of language. 
Hence we shall always be concerned with words, but 
only so far as they are the instruments for recording 
and referring to our thoughts. The grammarian also 
treats of language, but he treats it as language merely, 
and his science terminates with the description and ex- 
planation of the forms, varieties, and relations of 
words. Logic also treats of language, but only as the 
necessary index to the action of mind. 

Again, so long as we think correctly, we must think of things 
as they are. The state of mind within us must correspond to 
the state of things without us, whenever an opportunity arises 
for comparing them. It is impossible and inconceivable that iron 
should prove not to be an elementary substance, if it be a metal, 
and every metal be an element. We cannot suppose, and there 
is no reason to suppose, that by the constitution of the mind we 
are obliged to think of things differently from the manner in 
which they are. If, then, we may assume that things really 



13 INTRODUCTION. 

agree or differ, according as by correct logical thought we are in- 
duced to believe they will, it does not seem that the views of the 
logicians named are irreconcileable. We treat of things so far 
as they are the objects of thought, and we treat of language so 
far as it is the embodiment of thought. If the learner will bear 
this explanation in mind, he will be saved from some perplexity 
when he proceeds to read different works on logic, and finds them 
to vary exceedingly in the mode of treatment, or at least of ex- 
pression. 

11. The Three Logical Operations of Mind. 

If, when reduced to language, there be three parts of 
logic, terms, propositions, and syllogisms, there must be 
as many different kinds of thought or operations of 
mind. These are usually called — 

(1) Simple apprehension. 

(2) Judgment. 

(3) Eeasoning, or discourse. 

(1) Simple Apprehension is the act of mind by 
which we merely become aware of something, or have 
an idea or impression of it brought into the mind. The 
adjective simple means apart from other things, and 
apprehension the taking hold by the mind. Thus the 
name or term iron instantaneously makes the mind 
think of a strong and very useful metal, but does not 
tell us anything about it, or compare it with any thing 
else. The words sun, Jupiter, Sirius, St. PauVs Cathe- 
dral, are also terms which call up into the mind certain 
well-known objects, which dwell in our recollection even 
when they are not present to our senses. In fact, the 
use of a term, such as those given as examples, is 
merely as a substitute for the exhibition of the actual 
things named. 



INTRODUCTION. 13 

(2) Judgment is a different action of mind, and con- 
sists in comparing together two notions or ideas of ob- 
jects derived from simple apprehension, so as to ascer- 
tain whether they agree or differ. It is evident, there- 
fore, that we cannot judge or compare unless we are con- 
scious of two things, or have the notions of two things 
in the mind at the same time. Thus, if I compare Jupiter 
and Sirius, I first simply apprehend each of them ; but, 
bringing them into comparison, I observe that they 
agree in being small, bright, shining bodies, which rise 
and set and move round the heavens with apparently 
equal speed. By minute examination, however, I no- 
tice that Sirius gives a twinkling or intermittent light, 
whereas Jupiter shines steadily. More prolonged ob- 
servation shows that Jupiter and Sirius do not really 
move with equal and regular speed, but that the former 
changes its position upon the heavens from night to 
night in no very simple manner. If the comparison be 
extended to others of the heavenly bodies which are ap- 
prehended or seen at the same time, I shall find that 
there are a multitude of stars which agree with Sirius 
in giving a twinkling light and in remaining perfectly 
fixed in relative position to each other, whereas two or 
three other bodies may be seen which resemble Jupiter 
in giving a steady light, and also in changing their 
place from night to night among the fixed stars. I 
have now by the action of judgment formed in my mind 
the general notion op concept of fixed stars, by bringing 
together mentally a number of objects which agree ; 
while from several other objects I have formed the gen- 
eral notion of planets. Comparing the two general 
notions together, I find that they do not possess the 



14 INTRODUCTION. 

same qualities or appearances, which I state in the 
proposition, " Planets are not fixed stars." 

The expression " General Notion " is introduced as if the 
learner were fully acquainted with it. Bat though philosophers 
have, for more than two thousand years, constantly used the ex- 
pressions, general notion, idea, conception, concept, etc., they 
have never succeeded in agreeing exactly as to the meaning of 
the terms. One class of philosophers, called Nominalists, say 
that it is all a matter of names, and that when we join together 
Jupiter, Mars, Saturn, Venus, etc., and call them planets, the 
common name is the bond between them in our minds. Others, 
called Realists, have asserted that, besides these particular 
planets, there is really something which combines the properties 
common to them all, without any of the differences of size, 
Color, or motion which distinguish them. Every one allows in 
the present day, however, that nothing can physically exist cor- 
responding to a general notion, because it must exist here or 
there, of this size or of that size, and, therefore, it would be one 
particular planet, and not any planet whatever. The Nominal- 
ists, too, seem equally wrong, because language, to be of any use, 
must denote something, and must correspond, as we have seen, 
to acts of mind. If then proper names raise up in our minds the 
images of particular things, like Jupiter, etc., general names 
should raise up general notions. 

The true opinion seems to be that of the philosophers called 
Conceptualists, who say that the general notion is the knowledge 
in the mind of the common properties or resemblances of the 
things embraced under the notion. Thus, the notion planet 
really means the consciousness in anybody's mind that there are 
certain heavenly bodies which agree in giving a steady light and 
in moving about the heavens differently from the fixed stars. It 
should be added, however, that there are many, including Sir W. 
Hamilton, who would be counted as Nominalists, and who yet 
hold that with the general name is associated a consciousness of 
the resemblance existing between the things denoted by it. 
Between this form of the doctrine and conceptualism it is not 
easy to draw a precise distinction, and the subject is of too de- 
batable a character to be pursued in this work. 



INTKODUCTION. 15 

(3) Reasoning, or Discourse, may be defined as 
the progress of the mind from one or more given propo- 
sitions to a proposition different from those given. 
Those propositions from which we argue are called 
Premises, and that which is drawn from them is called 
the Conclusion. The latter is said to follow, to be con- 
cluded, inferred, or collected from them; and the 
premises are so called because they are put forward, or 
at the beginning (Latin prw, before, and mitto, I send 
or put). The essence of the process consists in gather- 
ing the truth that is contained in the premises when 
joined together, and carrying it with us into the con- 
clusion, where it is embodied in a new proposition or 
assertion. We extract out of the premises all the in- 
formation which is useful for the purpose in view — and 
this is the whole which reasoning accomplishes. 

It will appear in the course of our study that the whole of 
logic, and the whole of any science, consists in so arranging the 
individual things we meet in general notions or classes, and in 
giving them appropriate general names or terms, that our 
knowledge of them may be made as simple and general as 
possible. Every general notion that is properly formed admits 
of the statement of general laws or truths ; thus of the planets 
we may affirm that they move in elliptic orbits round the sun 
from west to east ; that they shine with the reflected light of the 
sun ; and so on. Of the fixed stars we may affirm that they 
shine with their own proper light ; that they are incomparably 
more distant than the planets ; and so on. The whole of reason- 
ing will be found to arise from this faculty of judgment, which 
enables us to discover and affirm that a large number of objects 
have similar properties, so that whatever is known of some may 
be inferred and asserted of others. 

It is in the application of such knowledge that we employ the 
third act of mind called discourse or reasoning, by which from 
certain judgments we are enabled, without any new reference to 






16 INTRODUCTION. 

the real objects, to form a new judgment. If we know that iron 
comes under the general notion of metal, and that this notion 
comes under the still wider notion of element, then, without 
further examination of iron, we know that it is a simple unde- 
composable substance called by chemists an element. Or if 
from one source of information we learn that Neptune is a 
planet, and from another that planets move in elliptic orbits, we 
can join these two portions of knowledge together in the mind, 
so as to elicit the truth that Neptune moves in an elliptic orbit. 

12. Method of Treatment. 

Simple apprehension is expressed in terms, judgment 
in propositions, and reasoning in syllogisms. The dis- 
cussion of these needs to be supplemented by the 
examination of fallacies and induction, some account of 
logical method, and a view of recent logical theories. 
Our chapters, therefore, will be as follows : 

1. Terms. 

2. Propositions* 

3. Syllogisms. 

4. Fallacies. 

5. Induction. 

6. Method. 

7. Recent Logical Views. 



L O Gr I C . 

CHAFTEE U 

TERMS. 

In tlie treatment of Terms we shall find it convenient 
to consider: (1) The Various Kinds of Terms ; 
(2) The Ambiguity of Terms; (3) The Two- 
fold Meaning of Terms 9 in Extension and In- 
tension ; (4) The Growth of Language ; and 
(5) The Perfect and the Imperfect Know- 
ledge of Terms, The discussion of these topics 
will occupy the following sections. 



SECTION I. 

THE VARIOUS KINDS OF TERMS. 

1. The Meaning- of "Term" Explained. 

It has been explained that every assertion or state- 
ment expresses the agreement or difference of two 
things, or of two general notions. In putting the 
assertion or statement into words, we must accordingly 
have words suitable for drawing the attention of the 
mind to the things which are compared, as well as 
words indicating the result of the comparison, that is 
to say, the fact whether they agree or differ. The 
words by which we point out the things or classes of 
things in question are called Terms, and the words 
denoting the comparison are said to form the Copula. 



18 TERMS. 

Hence a complete assertion or statement consists of 
two terms and a copula, and when thus expressed it 
forms a Proposition. Thus in the proposition "Dic- 
tionaries are useful books," the two terms are diction- 
aries and useful books ; the copula is the verb are, and 
expresses a certain agreement of the class dictionaries 
with the class of useful books consisting in the fact 
that the class of dictionaries forms part of the class of 
useful books. In this case each term consists of only 
one or two words, but any number of words may be 
required to describe the notions or classes compared 
together. In the proposition "the angles at the base 
of an isosceles triangle are equal to each other," the 
first term requires nine words for its expression, and 
the second term, four words (equal to each other) ; and 
there is no limit to the number of words which may be 
employed in the formation of a term. 

A Term is so called because it forms one end (Latin, terminus) 
of a proposition, and strictly speaking it is a term only so long as 
it stands in the proposition. But we commonly speak of a term 
or a name meaning any noun, substantive or adjective, or any 
combination of words denoting an object of thought, whether 
that be, as we shall shortly see, an individual thing, a group of 
things, a quality of things, or a group of qualities. It would be 
impossible to define a name or term better than has been done by 
Hobbes: "A name is a word taken at pleasure to serve for a 
mark, which may raise in our mind a thought like to some 
thought which we had before, and which, being pronounced to 
others, may be to them a sign of what thought the speaker had 
before in his mind." 

2. Categ'oreniatic and Syncategorematic Words. 

Though every term or name consists of words, it is 
not every word which can form a name by itself. We 






VAEIOUS KINDS OF TERMS. 19 

cannot properly say " Not is agreeable " or " Probably 
is not true ; " nothing can be asserted of a preposition, 
an adverb, and certain other parts of speech, except 
indeed that they are prepositions, adverbs, etc. No 
part of speech except a noun substantive, or a group of 
words used as a noun substantive, can form the subject 
or first term of a proposition, and nothing but a noun 
substantive, an adjective, the equivalent of an adjec- 
tive, or a verb, can form the second term or predicate 
of a proposition. It may indeed be questioned whether 
an adjective can ever form a term alone ; thus in " Dic- 
tionaries are useful," it may be said that the substan- 
tive things or hooks is understood in the predicate, 
the complete sentence being " Dictionaries are useful 
books ;" but as this is a disputed point we will assume 
that words are divided into two kinds in the following 
manner : — 

(1) Words which stand, or appear to stand, alone as 
complete terms, namely the substantive and adjective, 
and certain parts of a verb, are called Categorematic 
words, (from the Greek word Karrjyopeo)), to assert or 
predicate. 

(2) Those parts of speech, on the other hand, such 
as prepositions, adverbs, conjunctions, etc., which can 
only form parts of names or terms, are called Syncate- 
gorematic words, because they must be used with other 
words in order to compose terms (Greek ovv, with, and 
K.aT7}yope(o) . Of syncategorematic words we need not 
take further notice except so far as they form part of 
categorematic terms. 



20 TERMS. 



3. Singular Terms. 

Terms are distinguished into singular or individual, 
and general or common terms, this being a very obvious 
division, but one of much importance. A Singular 
term is one which can denote only a single object, so 
long at least as it is used in exactly the same meaning ; 
thus the Emperor of the French, the Atlantic Ocean, 
St. Paul's, William Shakspeare, the most precious of 
metals, are singular terms. All proper names belong 
to this class ; for though John Jones is the name 
of many men, yet it is used not as meaning any of 
these men, but some single man — it has, in short, a 
different meaning in each case, just as London in 
England, has no connection in meaning with London 
in Canada. 

4. General Terms. 

General terms are applicable in the same sense 
equally to any one of an indefinite number of objects 
which resemble each other in certain qualities. Thus 
metal is a general name because it may be applied 
indifferently to gold, silver, copper, tin, aluminium, 
or any of about fifty known substances. It is not the 
name of any one of these more than any other, and it 
is in fact applied to any substance which possesses 
metallic lustre, which cannot be decomposed, and 
which has certain other qualities easily recognized by 
chemists. Nor is the number of substances in the 
class restricted ; for as new kinds of metal are from 
time to time discovered they are added to the class. 
Again, while Mars, Jupiter, Saturn, etc., are singular 



VARIOUS KINDS OF TERMS. 21 

terms, since each can denote only a single planet, the 
term planet is a general one, being applicable to as 
many bodies as may be discovered to revolve round the 
sun as the earth does. 

5. Collective Terms. 

We must carefully avoid any confusion between 
general and collective terms. By a collective term we 
mean the name of a number of things when all joined 
together as one whole ; like the soldiers of a regiment, 
the men of a jury, the crew of a vessel ; thus a collec- 
tive term is the name of all, but not of each. A general 
term, on the other hand, is the name of a number of 
things, but of each of them separately, or, to use the 
technical expression, distributively. Soldier, juryman, 
sailor, are the general names which may belong to John 
Jones, Thomas Brown, etc., but we cannot say that 
John Jones is a regiment, Thomas Brown a jury, and 
so on. The distinction is exceedingly obvious when thus 
pointed out, but it may present itself in more obscure 
forms, and is then likely to produce erroneous reason- 
ing. It is easy to see that we must not divide terms 
into those which are general and those which are col- 
lective, because it will often happen that the same term 
is both general and collective, according as it is regard- 
ed. Thus, library is collective as regards the books in 
it, but is general as regards the great number of differ- 
ent libraries, private or public, which exist. 

Regiment is a collective term as regards the soldiers which 
compose it, but general as regards the hundred different regi- 
ments, the Coldstream Guards, the Highland regiment, the 



22 TERMS. 

Welsli Fusiliers, and the rest, which compose the British stand- 
ing army. Army, again, is a collective whole, as being composed 
of a number of regiments organized together. Year is collective 
as regards the months, weeks, or days of which it consists, but is 
general as being the name either of 1869 or 1870, or any period 
marked by a revolution of the earth round the sun. 

We have not always in the English language sufficient means 
of distinguishing conveniently between the general and collec- 
tive use of terms. In Latin this distinctive use was exactly 
expressed by omnes, meaning all distributively, and cuncti 
meaning all taken together, a contracted form of conjuncti 
(joined together). In English all men may mean any man or all 
men together. Even the more exact word every is sometimes 
misused, as in the old proverb, " Every little makes a mickle," 
where it is obvious that every little portion cannot by itself make 
much, but only when joined to other little poxtions. 

6. Concrete and Abstract Terms. 

An important distinction between terms is that of 
concrete terms and abstract terms; and it cannot be 
better described than in the words of Mr. Mill, by say- 
ing that a concrete name is the name of a thing, the 
abstract name is the name of a quality, attribute, or 
circumstance of a thing. Thus red house is the name 
of a physically-existing thing, and is concrete ; redness 
is the name of one quality of the. house, and is abstract. 
The word abstract means drawn from (Latin, abstrac- 
tus, from abstr cthere, to draw away from), and indi- 
cates that the quality redness is thought of in the mind 
apart from all the other qualities which belong to the 
red house, or other red object. But though we can 
think of a quality by itself, we cannot suppose that the 
quality can exist physically apart from the matter in 
which it is manifest to us. Eedness means either a 



VARIOUS KINDS OF TEEMS. 23 

notion in the mind, or it means that in red objects 
which excites the notion. 

The learner should carefully observe that adjectives are con- 
crete, not abstract. If we say that a hook is useful, it is to the 
book we apply the adjective useful, and usefulness is the abstract, 
noun which denotes the quality ; similarly, the adjectives equal, 
grateful, reverent, rational, are the names of things, and the 
corresponding abstract nouns are equality, gratitude, reverence, 
rationality. 

It is a good exercise to try to discover pairs of correspond- 
ing concrete and abstract names; thus animal has animality; 
miser, miserliness ; old, agedness, or old age ; substance, sub- 
stantiality ; soap, soapiness ; shrub, shrubbiness ; and so on. But 
it by no means follows that an abstract word exists for each con- 
crete ; table hardly has an abstract tabularity ; and though ink 
has inkiness, we should not find the abstract of pen. It is by 
the accidents of the history of language that we do or do not 
possess abstract names ; and there is a constant tendency to 
invent new abstract words in the progress of time and science. 

Unfortunately concrete and abstract names are frequently 
confused, and it is by no means always easy to distinguish the 
meanings. Thus relation properly is the abstract name for the 
position of two people or things to each other, and those people 
are properly called relatives (Latin, relativus, one who is related). 
Bat we constantly speak now of relations, meaning the persons 
themselves ; and when we want to indicate the abstract relation 
they have to each other we have to invent a new abstract name 
relationship. Nation has long been a concrete term, though from 
its form it was probably abstract at first; but so far does the 
abuse of language now go, especially in newspaper writing, that 
we hear of a nationality meaning a nation, although of course if 
nation is the concrete, nationality ought to be the abstract, 
meaning the quality of being a nation. Similarly, action, inten- 
tion, extension, conception, and a multitude of other properly 
abstract names, are used confusedly for the corresponding con- 
crete, namely, act, intent, extent, concept, etc. Production is 
properly the condition or state of a person who is producing or 



24 TERMS. 

drawing something forth ; hut it has now become confused with 
that which is produced, so that \vj constantly talk of the produc- 
tions of a country, meaning the products. The logical terms, 
Proposition, Deduction, Induction. Syllogism, are all properly 
abstract words, but are used concretely for a Proposition, a De- 
duction, an Induction, a Syllogism ; and it must be allowed that 
logicians are nearly as bad as other people in confusing abstract 
and concrete terms. Much injury is done to language by this 
abuse. 

7. Positive and Negative Terras. 

Another very obvious division of terms is between 
those which are positive, and those which are negative. 

The difference is usually described by saying that posi- 
tive terms signify the existence or possession of a 
quality, as in grateful, metallic, organic, etc., while 
the corresponding negatives signify the absence of the 
same qualities as in ungrateful, non-metallic, inorganic. 
The negative terms may be adjectives as above, or sub- 
stantives, concrete or abstract ; thus ingratitude, in- 
equality, inconvenience, are abstract negative terms; 
and individuals, unequals, etc., are concrete negatives. 
We usually consider as negative terms any which have 
a negative prefix such as not, non, un, in, etc. ; but 
there are a great many terms which serve as negatives 
without possessing any mark of their negative charac- 
ter. Darkness is the negative of light or lightness, 
since it means the absence of light ; compound is the 
negative of element, since we should give the name of 
compound to whatever can be decomposed, and element 
is what cannot be decomposed ; theoretically speaking 
every term has its corresponding negative, but it by no 
means follows that language furnishes the term ready- 



VARIOUS KINDS OF TERMS. 25 

made. Thus table has the corresponding adjective tab- 
ular, but there is no similar negative untabular ; one 
man may be called a bookworm, but there is no nega- 
tive for those who are not bookworms, because no need 
of the expression has been felt. A constant process of 
invention of new negative terms goes on more rapidly 
perhaps than is desirable, for when an idea is not 
often referred to it is better to express it by a phrase 
than add to the length of the dictionary by a new- 
created word. 

It would seem that in many cases a negative term implies the 
presence of some distinct quality or fact. Thus inconvenience 
doubtless implies the absence of convenience, but also the pres- 
ence of positive trouble or pain occasioned thereby. Unhappi- 
ness is a negative term, but precisely the same notion is 
expressed by the positive term misery. The negative of healthy 
is unhealthy, but the positive term sickly serves equally well. 
It thus appears to be more a matter of accident than anything 
else whether a positive or negative term is used to express any 
particular notion. All that we can really say is that every posi 
tive term necessarily implies the existence of a corresponding 
negative term, which may be the name of all those things to 
which the positive name cannot be applied. Whether this term 
has been invented or not is an accident of language ; its existence 
may be assumed in logic. 

The reader may be cautioned against supposing that every 
term appearing to be of a negative character on account of 
possessing a negative prefix is really so. The participle unloosed 
certainly appears to be the negative of loosed; but the two words 
mean exactly the same thing, the prefix un not being really the 
negative ; invaluable, again, means not what is devoid of value, 
but what is so valuable that the value cannot be measured ; and 
a shameless action can equally be called by the positive 
term, a shameful action. Other instances might no doubt be 
found. 

Great care should be taken to avoid confusing terms which 



26 TERMS. 

cxpivss the presence or absence of a quality with those which 
describe its degree. Less is not the negative of greater because 
there is a third alternative, equal. The true negative of greater 
is not-greater, and this is equivalent to either equal or less. So it 
may be said that disagreeable is not the simple negative of agree- 
able, because there may be things which are neither one nor the 
other, but are indifferent to us. It would not be easy to say off- 
hand whether every action which is not honest is dishonest, or 
whether there may not be actions of an intermediate character. 
The rule is that wherever the question is one of degree or quan- 
tity a medium is possible, and the subject belongs rather to the 
science of quantity than to simple logic ; where the question is 
one of the presence or absence of a quality, there cannot be more 
than two alternatives, according to one of the Primary Laws of 
Thought, which we will consider in Chap. Ill, Sec. I. In the 
case of quantity we may call the extreme terms opposites ; thus 
less is the opposite of greater, disagreeable of agreeable ; in the 
case of mere negation we may call the terms negatives or con- 
tradictories, and it is really indifferent in a logical point of 
view which of a pair of contradictory terms we regard as the 
positive and which as the negative. Each is the negative of the 
other. 

8. Privative Terms. 

Logicians have distinguished from simple negative 
terms a class of terms called privative, such as Mind, 
dead, etc. Such terms express that a thing has been 
deprived of a quality which it before possessed, or was 
capable of possessing, or usually does possess. A man 
may be born blind, so that he never did see, but he 
possesses the orgaus which would have enabled him to 
see except for some accident. A stone or a tree could 
not have had the faculty of seeing under any circum- 
stances. No mineral substance can properly be said to 
die or to be dead, because it was incapable of life ; but 



VARIOUS KINDS OF TEEMS. 27 

it may be called uncrystallized because it might have 
been in the form of a crystal. Hence we apply a 
privative term to anything which has not a quality 
which it was capable of having; we apply a negative 
term to anything which has not and could not have the 
quality. It is doubtful however whether this distinc- 
tion can be properly carried out, and it is not of very 
much importance. 

9. Relative and Absolute Terms. 

It is further usual to divide terms according as they 
are relative or absolute, that is, non-relative. The 
adjective absolute means whatever is- "loosed from con- 
nection with anything else " (Latin db, from, and 
solutus, loosed) ; whereas relative means that which is 
carried in thought, at least, into connection with some- 
thing else. Hence a relative term denotes an object 
which cannot be thought of without reference to some 
other object, or as part of a larger whole. A father 
cannot be thought of but in relation to a child, a 
monarch in relation to a subject, a shepherd in relation 
to a flock; thus father, monarch, and shepherd are 
relative terms, while child, subject, and flock are the 
correlatives (Latin con, with, and relativus), or those 
objects which are necessarily joined in thought with 
the original objects. The very meaning, in fact, of 
father is that he has a child, of monarch that he has 
subjects, and of shepherd that he has a flock. As 
examples of terms which have no apparent relation to 
anything else, I may mention water, gas, tree. There 
does not seem to me to be anything so habitually asso- 
ciated with water that we must think of it as part of 



28 TERMS. 

the same idea, and gas, tree, and a multitude of other 
terms also denote objects which have no remarkable or 
permanent relations such as would entitle the terms to 
be called relatives. They may therefore be considered 
absolute or non -relative terms. 

The fact, however, is that everything mu9t really have rela- 
tions to something else, the water to the elements of which it is 
composed, the gas to the coal from which it is manufactured, 
the tree to the soil in which it is rooted. By the very laws of 
thought, again, no thing or class of things can be thought of but 
by separating them from other existing things from which they 
differ. I cannot use the term mortal without at once separating 
all existing or conceivable things into the two groups mortal and 
immortal ; metal, element, organic substance, and every other 
term that could be mentioned, would necessarily imply the 
existence of a correlative negative term, non-metallic, compound, 
inorganic substance, and in this respect therefore every term is 
undoubtedly relative. Logicians, however, have been content to 
consider as relative terms those only which imply some peculiar 
and striking kind of relation arising from position in time or 
space, from connection of cause and effect, etc. ; and it is in this 
special sense therefore the student must use the distinction. 

10. Summary. 

The most important varieties of terms having been 
explained, it is desirable that the learner should acquire 
a complete familiarity with them by employing the exer- 
cises at the end of the book. The learner is to deter- 
mine concerning each of the terms there given: — 

1, Whether it is a categoremalic or a syncategore- 

matic word. 

2, Whether it is a general or a singular term, 

3, Whether it is collective or distributive, 

4, Whether it is concrete or abstract. 



VAKIOUS KINDS OF TERMS. 29 

5. Whether it is positive, or negative, or priva- 

tive. 

6. Whether it is relative or absolute. 

It will be fully pointed out in the next section that most 
terms have more than one meaning ; and as the one meaning 
may be general and the other singular, the one concrete and the 
other abstract, and so on, it is absolutely necessary that the 
learner should first of all choose one precise meaning of the 
term which he is examining. And in answering the questions 
proposed it is desirable he should specify the way in which he 
regards it. Taking the word sovereign, we may first select the 
meaning in which it is equivalent to monarch ; this is a general 
term in so far as it is the name of any one of many monarchs 
living or dead, but it is singular as regards the inhabitants of any 
one country. It is clearly categorematic, concrete, and positive, 
and obviously relative to the subjects of the monarch. 

Read Mr. Mill's chapter on Names, System of Logic, Book I, 
chap. 2. 

In this section on te Various Kinds of Terms," 
we have considered:— 

1. The Meaning of " Term." 

2. Categorem atic and Syncategorematic Words. 

3. Singular Terms. 

4. General Terms. 

5. Collective Terms. 

6. Concrete and Abstract Terms. 

7. Positive and Negative Terms. 

8. Privative Terms. 

9. Relative and Absolute Terms. 



30 TERMS. 

SECTION II. 

THE AMBIGUITY OF TERMS. 

1. Importance of Avoiding Ambiguity. 

There is no part of Logic which is more really useful 
than that which treats of the ambiguity of terms, that 
is, of the uncertainty and variety of meanings belong- 
ing to words. Nothing indeed can be of more impor- 
tance to the attainment of correct habits of thinking 
and reasoning than a thorough acquaintance with the 
great imperfections of language. Comparatively few 
terms have one single clear meaning and one meaning 
only, and whenever two or more meanings are uncon- 
sciously confused together, we inevitably commit a 
logical fallacy. If, for instance, a person should argue 
that "punishment is an evil," and according to the 
principles of morality " no evil is to be allowed even with 
the purpose of doing good," we might not at the first 
moment see how to avoid the conclusion that " no pun- 
ishments should be allowed," because they cause evil. 
A little reflection will show that the word evil is here 
used in two totally different senses ; in the first case it 
means physical evil or pain ; in the second, moral evil ; 
and because moral evil is never to be committed, it does 
not follow that physical evils are never to be inflicted, 
for they are often the very means of preventing moral 
evil. 

Another very plausible fallacy which has often been put 
forth in various forms is as follows : " A thoroughly benevolent 
man cannot possibly refuse to relieve the poor, and since a per- 
son who cannot possibly act otherwise than he does can claim no 



THE AMBIGUITY OF TERMS. 31 

merit for his actions, it follows that a thoroughly benevolent man 
can claim no merit for his actions." According to this kind of 
argument a man would have less merit in proportion as he was 
more virtuous, so as to feel greater and greater difficulty in act- 
ing wrongly. That the conclusion is fallacious every one must 
feel certain ; but the cause of the fallacy can only be detected by 
observing that the words cannot possibly have a double meaning, 
in the first case referring to the influence of moral motives or 
good character, and in the second to circumstances entirely be- 
yond a person's control ; as, for instance, the compulsion of the 
laws, the want of money, the absence of personal liberty. The 
more a person studies the subtle variations in the meaning of 
cornmon words, the more he will be convinced of the dangerous 
nature of the tools he has to use in all communications and argu- 
ments. Hence the learner should give much attention to the 
contents of this section. 

2. Univocal and Equivocal Terms. 

Terms are said to be univocal when they can suggest 
to the mind no more than one single definite meaning. 
They are called equivocal or ambiguous when they have 
two or more different meanings. It will be observed, 
however, that a term is not equivocal because it can be 
applied to many objects when it is applied in the same 
sense or meaning to those different objects. Thus 
cathedral is the name of St. Paul's, the York Minster, 
and the principal churches of Salisbury, Wells, Lincoln 
and a number of other cities, but it is not ambiguous, 
because all these are only various instances of the same 
meaning ; they are all objects of the same description 
or kind. The word cathedral is probably univocal or 
of one logical meaning only. The word church, on the 
other hand, is equivocal, because it sometimes means 
the building in which religious worship is performed, 



32 TEEMS. 

sometimes the body of persons who belong to one sect 
or persuasion, and assemble in churches. Sometimes 
also the church means the body of the clergy as distin- 
guished from the laity ; hence there is a clear differ- 
ence in the sense or meaning with which the word is 
used at different times. 

Instances of univocal terms are to be found chiefly in technical 
and scientific language. Steam-engine, gasometer, railway train, 
permanent way, and multitudes of such technical names denot- 
ing distinct common objects, are sufficiently univocal. In com- 
mon life the names penny, mantelpiece, teacup, bread and butter, 
have a sufficiently definite and single meaning. So also in chem- 
istry, oxygen, hydrogen, sulphate of copper, alumina, lithia, and 
thousands of other terms, are very precise, the words themselves 
having often been invented in very recent years, and the mean- 
ings exactly fixed and maintained invariable. Every science 
has, or ought to have, a series of terms equally precise and cer- 
tain in meaning. The names of individual objects, buildings, 
events, or persons, again, are usually quite certain and clear, 
as Julius Caesar, William the Conqueror, the first Napoleon, 
Saint Peter's, Westminster Abbey, the Great Exhibition of 1851, 
and so on. 

But however numerous may be the univocal terms which can 
be adduced, still the equivocal terms are astonishingly common. 
They include most of the nouns and adjectives which are in 
habitual use ii/tlie ordinary intercourse of life. They are called 
ambiguous from the Latin verb ambigo, to wander, hesitate, or 
be in doubt ; or again homonymous, from the Greek ojwc, like, 
and bvoiia, name. Whenever a person uses equivocal words in 
such a way as to confuse the different meanings and fall into 
error, he may be said to commit the fallacy of Equivocation in 
the logical meaning of the name (see Chapter IV) ; but in com- 
mon life a person is not said to equivocate unless he uses words 
consciously and deceitfully in a maimer calculated to produce a 
confusion of the true and apparent meanings. 



THE AMBIGUITY OF TERMS. 33 



3. Kinds and Causes of Ambiguity, 

Following Dr. Watts in classifying equivocal words, 
we may distinguish three classes according as they are — 

>. Equivocal in sound only. 

2. Equivocal in spelling only. 

3. Equivocal in both sound and spelling. 

The first two classes are comparatively speaking of very 
slight importance, and do not often give rise to serious 
error. They produce what we should call trivial mis- 
takes. Thus we may confuse, when spoken only, the 
words right, wright, and rite (ceremony) ; also the words 
rein, rain and reign, might and mite, etc. Owing 
partly to defects of pronunciation mistakes are not 
unknown between the four words air, hair, hare and 
heir. 

Words equivocal in spelling but not in sound are 
such as tear (a drop), and tear pronounced tare, mean- 
ing a rent in cloth ; or lead, the metal, and lead, as in 
following the lead of another person. As little more 
than momentary misapprehension, however, can arise 
from such resemblance of words, we shall pass at once 
to the class of words equivocal both in sound and spell- 
ing. These I shall separate into three groups accord- 
ing as the equivocation arises — 

1. From the accidental confusion of different words. 

2. From the transfer of meaning by the association 

of ideas. 

3. From the logical transfer of meaning to analogous 

objects. 



34 TERMS. 

(1) Under the first class we place a certain number 
of curious but hardly important cases in which ambi- 
guity has arisen from the confusion of entirely different 
words, derived from different languages or from differ- 
ent roots of the same language, but which have in the 
course of time assumed the same sound and spelling. 
Thus the word mean denotes either that which is 
medium or mediocre, from the French moyen and the 
Latin medius, connected with the Anglo-Saxon mid, 
or middle ; or it denotes what is low-minded and base, 
being then derived from the Anglo-Saxon Oemcene, 
which means "that belonging to the moene or many," 
whatever in short is vulgar. The verb to mean can 
hardly be confused with the adjective mean, but it 
comes from a third distinct root, probably connected 
with the Sanscrit verb, to think. 

As other instances of this casual ambiguity, I may mention 
rent, a money payment, from the French rente (rendre, to return), 
or a tear, the result of the action of rending, this word being of 
Anglo-Saxon origin and one of the numerous class beginning in 
r or wr, which imitate more or less perfectly the sound of the 
action which they denote. Pound, from the Latin pondus, a 
weight, is confused with pound, in the sense of a village pinfold 
for cattle, derived from the Saxon pyndan, to pen up. Fell, a 
mountain, is a perfectly distinct word from fell, a skin or hide; 
and pulse, a throb or beating, and pulse, peas, beans, or potage, 
though both derived from the Greek or Latin, are probably quite 
unconnected words. It is curious that gin, in the meaning of 
trap or machine, is a contracted form of engine, and when denot- 
ing the spirituous liquor is a corruption of Geneva, the place 
where the spirit was first made. 

Certain important cases of confusion have been detected in 
grammar, as between the numeral one, derived from an Aryan 
root, through the Latin unus, and the indeterminate pronoun, 
one (as in " one ought to do one's duty"), which is really a corrupt 



THE AMBIGUITY OF TERMS. 35 

form of the French word homme or man. The Germans to the 
present day use man in this sense, as in man sagt, i. e. one says. 

(2) By far the largest part of equivocal words have 
become so by a transfer of the meaning from the thing 
originally denoted by the word to some other thing 
habitually connected with it so as to become closely 
associated in thought. Thus, in Parliamentary lan- 
guage, the House means either the chamber in which 
the members meet, or it means the body of members 
who happen to be assembled in it at any time. Simi- 
larly, the word church originally denoted the building 
(Kvpiatcov, the Lord's House) in which any religious 
worshippers assemble, but it has thence derived a 
variety of meanings ; it may mean a particular body of 
worshippers accustomed to assemble in any one place, 
in which sense it is used in Acts xiv. 23 ; or it means 
any body of persons holding the same opinions and 
connected in one organization, as in the Anglican, or 
Greek, or Eoman Catholic Church ; it is also sometimes 
used so as to include the laity as well as the clergy; 
but more generally perhaps the clergy and religious 
authorities of any sect or country are so strongly asso- 
ciated with the act of worship as to be often called the 
church par excellence. It is quite evident, moreover, 
that the word entirely differs in meaning according as 
it is used by a member of the Anglican, Greek, Eoman 
Catholic, Scotch Presbyterian, or any other existing 
church. 

The word foot has suffered several curious but very evident 
transfers of meaning. Originally it denoted the foot of a man 
or an animal, and is probably connected in a remote manner with 
the Latin pes, pedis, and the Greek irovg, nodoc ; but since the 



36 TERMS. 

length of the foot is naturally employed as a rude measure of 
length, it came to be applied to a fixed measure of length ; and 
as the foot is at the bottom of the body the name was extended 
by analogy to the foot of a mountain, or the feet of a table ; by a 
further extension, any position, plan, reason, or argument on 
which we place ourselves and rely, is called the foot or footing. 
The same word also denotes soldiers who fight upon their feet, 
or infantry, and the measured part of a verse having a definite 
length. That these very different meanings are naturally con- 
nected with the original meaning is evident from the fact that 
the Latin and Greek words for foot are subject to exactly similar 
series of ambiguities. 

It would be a long task to trace out completely the various 
and often contradictory meanings of the word fellow. Originally 
a fellow was what follows another, that is a companion ; thus it 
came to mean the other of a pair, as one shoe is the fellow of the 
other, or simply an equal, as when we say that Shakespeare 
"hath not a fellow." From the simple meaning of companion 
again it comes to denote vaguely a person, as in the question 
" What fellow is that? " but then there is a curious confusion of 
depreciatory and endearing power in the word ; when a man is 
called a mere fellow, or simply a fellow in a particular tone of 
voice, the name is one of severe contempt ; alter the tone of 
voice of the connected words in the least degree, and it becomes 
one of the most sweet and endearing appellations, as when we 
speak of a dear or good fellow. We may still add the technical 
meanings of the name as applied in the case of a Fellow of a 
College, or of a learned society. 

Another good instance of the growth of a number of different 
meanings from a single root is found in the word post. Origi- 
nally a post was something posited, or placed firmly in the ground, 
such as an upright piece of wood or stone ; such meaning still 
remains in the cases of a lamp-post, a gate-post, signal-post, etc. 
As a post would often be used to mark a fixed spot of ground, as 
in a mile-post, it came to mean the fixed or appointed place 
where the post was placed, as in a military post, the post of dan- 
ger or honor, etc. The fixed places where horses were kept in 
readiness to facilitate rapid travelling during the times of the 



THE AMBIGUITY OF TERMS. 37 

Roman empire were thus called posts, and thence the whole 
system of arrangement for the conveyance of persons or news 
came to be called the posts. The name has retained an exactly 
similar meaning to the preseDt da* T in most parts of Europe, and 
we still use it in post-chaise, post-boy, post-horse and postillion. 
A system of post conveyance for letters having been organized 
for about two centuries in England and other countries, this is 
perhaps the meaning most closely associated with the word post 
at present, and a number of expressions have thus arisen, such 
as post-office, postage, postal-guide, postman, postmaster, postal- 
telegraph, etc. Curiously enough we now have iron letter-posts, 
in which the word post is restored exactly to its original meaning. 
Although the words described above were selected on account 
of the curious variety of their meanings, I do not hesitate to 
assert that the majority of common nouns possess various 
meanings in greater or less number. Dr. Watts, in his Logic, 
suggests that the words book, bible, fish, house, and elephant, are 
univocal terms, but the reader would easily detect ambiguities 
in each of them. Thus fish bears a very different meaning in 
natural history from what it does in the mouths of unscientific 
persons, who include under it not only true fishes, but shell-fish 
or mollusca, and the cetacea, such as whales and seals, in short 
all swimming animals, whether they have the character of true 
fish or not. Elephant, in a stationer's or bookseller's shop, means 
a large kind of paper instead of a large animal. Bible some- 
times means any particular copy of the Bible, sometimes the 
collection of works constituting the Holy Scriptures. The word 
man is singularly ambiguous ; sometimes it denotes man as 
distinguished from woman ; at other times it is certainly used to 
include both sexes ; and in certain recent election cases lawyers 
were unable to decide whether the word man as used in the 
Reform Act of 1867 ought or ought not to be interpreted so as to 
include women. On other occasions man is used to denote an 
adult male as distinguished from a boy, and it also often denotes 
one who is emphatically a man as possessing a masculine char- 
acter. Occasionally it is used in the same way as groom, for a 
servant, as in the proverb, "Like master, like man." At other 
times it stands specially for a husband. 



38 TERMS. 

(3) Among ambiguous words we must, thirdly, dis- 
tinguish those which derive their various meanings in 
a somewhat different manner, namely by analogy or 
real resemblance. When we speak of a sweet taste, a 
sweet flower, a sweet tune, a sweet landscape, a sweet 
face, a sweet poem, it is evident that we apply one and 
the same word to very different things ; such a con- 
crete thing as lump-sugar can hardly be compared 
directly with such an intellectual existence as Tenny- 
son's May Queen. Nevertheless if the word sweet is to 
be considered ambiguous, it is in a different way from 
those we have before considered, because all the things 
are called sweet on account of a peculiar pleasure which 
they yield, which cannot be described otherwise than 
by comparison with sugar. 

In a similar way, we describe a pain as sharp, a disappoint- 
ment as bitter, a person's temper as sour, the future as bright or 
gloomy, an achievement as brilliant ; all these adjectives imply- 
ing comparison with bodily sensations of the simplest kind. 
The adjective brilliant is derived from the French briller, to 
glitter or sparkle ; and this meaning it fully retains when we 
speak of a brilliant diamond, a brilliant star, etc. By what a 
subtle analogy is it that we speak of a brilliant position, a 
brilliant achievement, brilliant talents, brilliant style ! We 
cannot speak of a clear explanation, indefatigable perseverance, 
perspicuous style, or sore calamity, without employing in each 
of these expressions a double analogy to physical impressions, 
actions, or events. It will be shown in the fourth section that 
to this process we owe the creation of all names connected with 
mental feelings or existences. 

Read Watts' Logic, Chapter IV. 

Locke's Essay on the Human Understanding, Book III, 
Chapters IX and X. 






EXTENSION" AND INTENSION. 39 

In this section, on the Ambiguity of Terms, we 
have considered :— 

1. Importance of Avoiding Ambiguity. 

2. Univocal and Equivocal Terms. 

3. Kinds and Causes of Ambiguity. 



SECTION III. 
EXTENSION AND INTENSION. 

1. Importance of Understanding this Double 
Meaning. 

There is no part of the doctrines of Logic more 
necessary to be understood than the twofold meaning 
of terms in extension and intension. The learner who 
acquires a thorough apprehension of the difference of 
these meanings, and learns to bear it always in mind, 
will experience but little further difficulty in the study 
of Logic. 

2. Meaning of Extension and Intension. 

The meaning of a term in extension consists of the 
objects to which the term may be applied ; its meaning 
in intension consists of the qualities which ape necessa- 
rily possessed by objects bearing that name. A simple 
example will make this distinction most apparent. 
What is the meaning of the name "metal"? The first 
and most obvious answer is that metal means either 
gold, or silver, or iron, or copper, or aluminium, or 
some other of the 48 substances known to chemists, 



40 TERMS. 

and considered to have a metallic nature. These sub- 
stances then form the plain and common meaning of 
the name, which is the meaning in extension. But if 
it he asked why the name is applied to all these sub- 
stances and these only, the answer must be — Because 
they possess certain qualities which belong to the nature 
of metal. We cannot, therefore, know to what sub- 
stances we may apply the name, or to what we may not, 
unless we know the qualities which are indispensable to 
the character of a metal. Now chemists lay these down 
to be somewhat as follows : — (1) A metal must be an 
element or simple substance incapable of decomposition 
or separation into simpler substances by any known 
means. (2) It must be a good conductor of heat and 
electricity. (3) It must possess a great and peculiar 
reflective power known as metallic lustre.* 

These properties are common to all metals, or nearly 
all metals, and are what mark out and distinguish a 
metal from other substances. Hence they form in a 
certain way the meaning of the name metal, the mean- 
ing in intension, as it is called, to distinguish it from 
the former kind of meaning. 

In a similar manner almost any other common name has a 
double meaning. " Steamship " denotes in extension the Great 
Eastern, the Persia, the Himalaya, or any one of the thousands 
of steamships existing or which have existed ; in intension it 
means " a vessel propelled by steam-power." Monarch is the 
name of Queen Victoria, Victor Emmanuel, Louis Napoleon, or 
any one of a considerable number of persons who rule singly 

* It is doubtfully true that all metals possess metallic lustre, and chemists 
would find it very difficult to give any consistent explanation of their use 
of the name ; hut the statements in the text are sufficiently true to furnish an 
example. 



EXTENSION AND INTENSION. 41 

over countries ; the persons themselves form the meaning in 
extension ; the quality of ruling alone forms the intensive mean- 
ing of the name. Animal is the name in extension of any one of 
billions of existing creatures and of indefinitely greater numbers 
of other creatures that have existed or will exist ; in intension it 
implies in all those creatures the existence of a certain animal 
life and sense, or at least the power of digesting food and exert- 
ing force, which are the marks of animal nature. 

3. Forms of Expressing Extension and Intension. 

It is desirable to state here that this distinction of 
extension and intension has been explained by logicians 
under various forms of expression. It is the peculiar 
misfortune of the science of logic to have a superfluity 
of names or synonyms for the same idea. Thus the 
intension of a term is synonymous with its comprehen- 
sion, or connotation, or depth ; while the extension is 
synonymous with the denotation or breadth. This may 
be most clearly stated in the form of a scheme : — 

The extension, extent, The intension, intent, 

breadth, denotation, do- depth, connotation, or im- 

main, sphere or application plication of a name con- 

of a name consists of the sists of the qualities the 

individual things to which possession of which by those 

the name applies. things is implied. 

Of these words, denotation and connotation are employed 
chiefly by Mr. J. S. Mill among modern logical writers, and are 
very apt for the purpose. To denote is to mark doion, and the 
name marks the things to which it may be applied or affixed ; 
thus metal denotes gold, silver, copper, etc. To connote is to 
mark along with (Latin con, together ; notare, to mark), and the 
connotation accordingly consists of the qualities before described, 
the possession of which is implied by the use of the name metal. 



42 TERMS. 

4. The Variation of Extension and Intension. 

When we compare different but related terms we may 
observe that they differ in the quantity of their exten- 
sion and intension. Thus the term element has a 
greater extension of meaning than metal, because it 
includes in its meaning all metals and other substances 
as well. But it has at the same time less intension of 
meaning ; for among the qualities of a metallic substance 
must be found the qualities of an element, besides the 
other qualities peculiar to a metal. If again we com- 
pare the terms metal and malleable metal, it is apparent 
that the latter term does not include the metals anti- 
mony, arsenic, and bismuth, which are brittle sub- 
stances. Hence malleable metal is a term of narrower 
meaning in extension than metal; but it has also 
deeper meaning in intension, because it connotes or 
implies the quality of malleability in addition to the 
general qualities of a metal. White malleable metal is 
again a narrower term in extension because it does not 
include gold and copper; and I can go on narrowing 
the meaning by the use of qualifying adjectives until 
only a single metal should be denoted by the term. 

5. The Law of Variation. 

The learner will now see clearly that a general law of 
great importance connects the quantity of extension 
and the quantity of intension, viz.— As the intension of 
a term is increased the extension is decreased. It 
must not be supposed, indeed, that there is any exact 
proportion between the degree in which one meaning 



EXTENSION" AND INTENSION. 43 

is increased and the other decreased. Thus if we join 
the adjective red to metal we narrow the meaning much, 
more than if we join the adjective white, for there are 
at least twelve times as many white metals as red. 
Again, the term white man includes a considerable 
fraction of the meaning of the term man as regards 
extension, but the term blind man only a small frac- 
tion of the meaning. Thus it is obvious that in 
increasing the intension of a term we may decrease the 
extension in any degree. 

In understanding this law we must carefully discriminate the 
cases where there is only an apparent increase of the intension 
of a term, from those where the increase is real. If I add the 
term elementary to metal, I shall not really alter the extension 
of meaning, for all the metals are elements ; and the elementary 
metals are neither more nor less numerous than the metals. But 
then the intension of the term is really unaltered at the same 
time ; for the quality of an element is really found among the 
qualities of metal, and it is superfluous to specify it over again. 
A quality which belongs invariably to the whole of a class of 
things is commonly called a property of the class, and we cannot 
qualify or restrict a term by its own property. 

6. Coimotative and Non-connotative Terms. 

This is a convenient place to notice a distinction 
between terms into those which are connotative and 
those which are non-connotative. the latter consisting 
of the terms which simply denote things without imply- 
ing any knowledge of their qualities. 

As Mr. Mill considers this distinction to be one of great 
importance, it will be well to quote his own words : — 

"A non-connotative term is one which signifies a subject only, 
or an attribute only. A connotative term is one which denotes a 



44 TERMS. 

subject, and implies an attribute. By a subject is here meant 
anything which possesses attributes. Thus John, or London, or 
England, are names which signify a subject only. Whiteness, 
length, virtue, signify an attribute only. None of these names, 
therefore, are connotative. But white, long, virtuous, are eonno- 
tative. The word white denotes all white things, as snow, paper, 
the foam of the sea, etc., and implies, or, as it was termed by the 
schoolmen, connotes the attribute whiteness. The word white is 
not predicated of the attribute, but of the subjects, snow, etc. ; 
but when we predicate it of them, we imply, or connote, that the 
attribute whiteness belongs to them 

"All concrete general names are connotative. The word 
man, for example, denotes Peter, James, John, and an indefinite 
number of other individuals, of whom, taken as a class, it is 
the name. But it is applied to them, because they possess, and 

to signify that they possess, certain attributes What we call 

men, are the subjects, the individual Styles and Nokes ; not the 
qualities by which their humanity is constituted. The name, 
therefore, is said to signify the subjects directly, the attributes 
indirectly ; it denotes the subjects, and implies, or involves, or 
indicates, or, as we shall say henceforth, connotes, the attri- 
butes. It is a connotative name 

"Proper names are not connotative: they denote the indi 
viduals who are called by them ; but they do not indicate or im- 
ply any attributes as belonging to those individuals. When we 
name a child by the name Paul, or a dog by the name Cassar, 
these names are simply marks used to enable those individuals 
to be made subjects of discourse. It may be said, indeed, that 
we must have had some reason for giving them those names 
rather than any others ; and this is true ; but the name, once 
given, is independent of the reason. A man may have been 
named John, because that was the name of his father; a town 
may have been named Dartmouth, because it is situated at the 
mouth of the Dart. But it is no part of the signification of the 
word John, that the father of the person so called bore the same 
name ; nor even of the word Dartmouth, to be situated at the 
mouth of the Dart. If sand should choke up the mouth of the 
river, or an earthquake change its course, or remove it to a dis- 






EXTENSION AND INTENSION. 45 

tance from the town, the name of the town would not necessarily 
be changed. " * 

I quote this in Mr. Mill's own words, because though it ex- 
presses most clearly the view accepted by Mr. Mill and many 
others, it is nevertheless probably erroneous. The connotation 
of[a name is confused with the etymological meaning, or the cir- 
cumstances which caused it to be affixed to a thing. Surely no 
one who uses the name England, and knows what it denotes, can 
be ignorant of the peculiar qualities and circumstances of the 
country, and these form the connotation of the term. To any 
one who knows the town Dartmouth the name must imply the 
possession of the circumstances by which that town is character- 
ized at the present time. If the river Dart should be destroyed 
or removed, the town would so far be altered, and the significa- 
tion of the name changed. The name would no longer denote a 
town situated on the Dart, but one which was formerly situated 
on the Dart, and it would be by a mere historical accident that the 
form of the name did not appear suitable to the town. So again 
any proper name, such as John Smith, is almost without meaning 
until we know the John Smith in question. It is true that the 
name alone connotes the fact that he is a Teuton, and is a male ; 
but, so soon as we know the exact individual it denotes, the 
name surely implies, also, the peculiar features, form, and charac- 
ter, of that individual. In fact, as it is only by the peculiar 
qualities, features, or circumstances of a thing, that we can 
ever recognize it, no name could have any fixed meaning unless 
we attached to it, mentally at least, such a definition of the kind 
of thing denoted by it, that we should know whether any given 
thing was denoted by it or not. If the name of John Smith does 
not suggest to my mind the qualities of John Smith, how shall I 
know him when I meet him ? for he certainly does not bear his 
name written upon his brow. 

Abstract names, on the other hand, can hardly possess conno- 
tation at all, for as they already denote the attributes or qualities 
of something, there is nothing left which can form the connota- 
tion of the name. Mr. Mill, indeed, thinks that abstract names 

* System of Logic, Vol. I, p. 31, sixth edition. Book I, Chap. n. 



46 TEEMS. 

may often be considered connotative, as when the name fault 
connotes the attribute of hurtfulness as belonging to fault. But 
if fault is a true abstract word at all I should regard hurtfulness 
as a part of its denotation ; I am inclined to think that faultiness 
is the abstract name, and that fault is generally used concretely 
as the name Of a particular action or thing that is faulty, or pos- 
sesses faultiness. But the subject cannot be properly discussed 
here, and the reader should note Mr. Mill's opinion that abstract 
names are usually non-connotative, but may be connotative in 
some cases. 

The subject of Extension and Intension may be pursued in 

Hamilton's Lectures on Logic, Lect. VIII. ; or in Thorn 

son's Laws of Thought, Sections 48 to 52. 

In this section, on Extension and Intension, we 
have considered :— 

1. The Importance of Understanding this Double 

Meaning, 

2. The Meaning of Extension and Intension. 

3. The Forms of Expressing Extension and In- 

tension. 

4. The Variation of Extension and Intension. 

5. The Law of Variation. 

6. Connotative and Non-connotative Terms. 



SECTION IY. 

THE GROWTH OF LANGUAGE. 

1. The Two Principal Processes of Growth. 

Words, we have seen, become equivocal in at least 
three different ways — by the accidental confusion of 
different words, by the change of meaning of a word 
by its habitual association with other things than its 
original meaning, and by analogical transfer to objects 
of a similar nature. We must, however, consider some- 



THE GROWTH OF LANGUAGE. 47 

what more closely certain changes in language which 
arise out of the last cause, and which are in constant 
progress. We can almost trace, in fact, the way in 
which language is created and extended, and the sub- 
ject is to the logician one of a highly instructive and 
important character. There are two great and con- 
trary processes which modify language, as follows : 

(1) Generalization, by which a name comes to be 
applied to a wider class of objects than before, so that 
the extension of its meaning is increased, and the in- 
tension diminished. 

(2) Specialization, by which a name comes to be 
restricted to a narrower class, the extension being de- 
creased and the intension increased. 

2. Generalization. 

The first change arises in the most obvious manner, 
from our detecting a resemblance between a new object, 
which is without a name, and some well-known object. 
To express the resemblance we are instinctively led to 
apply the old name to the new object. Thus we are 
well acquainted with glass, and, if we meet any sub- 
stance having the same glassy nature and appearance, 
we shall be apt at once to call it a kind of glass ; should 
we often meet with this new kind of glass it would 
probably come to share the name equally with the old 
and original kind of glass. The word coal has under- 
gone a change of this kind ; originally it was the name 
of charked or charred wood, which was the principal 
kind of fuel used five hundred years ago. As mineral 
coal came into use it took the name from the former 
fuel, which it resembled more nearly than anything 
else, but was at first distinguished as sea-coal or pit- 



48 TERMS. 

coal. Being now far the more common of the two, it 
has taken the simple name, and we distinguish charred 
wood as charcoal. Paper has undergone a like change ; 
originally denoting the papyrus used in the Roman 
empire, it was transferred to the new writing material 
made of cotton or linen rags, which was introduced at 
a quite uncertain period. The word character is inter- 
esting on account of its logical employment ; the Greek 
XapaicTfjp denoted strictly a tool for engraving, but it 
became transferred by association to the marks or letters 
engraved with it, and this meaning is still retained by 
the word when we speak of Greek characters, Arabic 
characters, i. e., figures or letters. But inasmuch as 
objects often have natural marks, signs, or tokens, 
which may indicate them as well as artificial characters, 
the name was generalized, and now means any peculiar 
or distinctive mark or quality by which an object is 
easily recognized. 

Changes of this kind are usually effected by no particular per- 
son and with no distinct purpose, but by a sort of unconscious 
instinct in a number of persons using the name. In the language 
of science, however, changes are often made purposely, and 

with a clear apprehension of the generalization implied. Thus 
soap in ordinary life is applied only to a compound of soda or 
potash with fat ; but chemists have purposely extended the name 
so as to include any compound of a metallic salt with a fatty sub- 
stance. Accordingly there are such things as lime-soap and lead- 
soap, which latter is employed in making common diachylon 
plaster. Alcohol at first denoted the product of ordinary fermen- 
tation commonly called spirits of wine, but chemists having dis- 
covered that many other substances had a theoretical composition 
closely resembling spirits of wine, the name was adopted for the 
whole class, and a long enumeration of different kinds of alco- 
hols will be found in Dr. Roscoe's lessons on chemistry. The 



THE GROWTH OF LANGUAGE. 49 

number of known alcohols is likewise subject to indefinite increase 
by tlie progress of discovery. Every one of the chemical terms 
acid, alkali, metal, alloy, earth, ether, oil, gas, salt, may be 
shown to have undergone great generalizations. In other 
sciences there is hardly a less supply of instances. A lens 
originally meant a lenticular shaped or double convex piece of 
glass, that being the kind of glass most frequently used by 
opticians. But as glasses of other shapes came to be used along 
with lenses, the name was extended to concave or even to per- 
fectly flat pieces of glass. The words lever, plane, cone, cylinder, 
arc, conic section, curve, prism, magnet, pendulum, ray, light, and 
many others, have been similarly generalized. 

In common language we may observe that even proper or 
singular names are often generalized, as when in the time of 
Cicero a good actor was called a Roscius after an actor of pre- 
eminent talent. The name Caesar was adopted by the successor 
of Julius Caesar as an official name of the emperor, with which it 
gradually became synonymous, so that in the present day the 
Kaisers of Austria and the Czars of Russia both take their title 
from Caesar. Even the abstract name Caesarism has been formed 
to express a kind of imperial system as established by Caesar. 
The celebrated tower built by a king of Egypt on the island of 
Pharos, at the entrance of the harbor of Alexandria, has caused 
lighthouses to be called phares in French, and pharos in obsolete 
English. From the celebrated Roman General Quintus Fabius 
Maximus any one who avoids bringing a contest to a crisis is said 
to pursue a Fabian policy. 

In science also singular names are often extended, as when 
the fixed stars are called distant suns, or the companions of 
Jupiter are called his moons, H is indeed one theory, and a 
probable one, that all general names were created by the process 
of generalization going on in the early ages of human progress. 
As the comprehension of general notions requires higher intellect 
than the apprehension of singular and concrete things, it seems 
natural that names should at first denote individual objects, and 
should afterwards be extended to classes. We have a glimpse 
of this process in the case of the Australian natives who had 
been accustomed to call a large dog Cadli, but when horses were 
3 



50 TERMS. 

first introduced into the country they adopted this name as the 
nearest description of a horse. A very similar incident is re- 
lated by Captain Cook of the natives of Otaheite. It may be ob- 
jected, however, that a certain process of judgment must have 
been exerted before the suitability of a name to a particular 
thing could have been perceived, and it may be considered 
probable that specialization as well as generalization must have 
acted in the earliest origin of language much as it does at 
present. 

3. Specialization. 

Specialization is an exactly opposite process to gener- 
alization and is almost equally important. It consists 
in narrowing the extension of meaning of a general 
name, so that it comes to be the name only of an 
individual or a minor part of the original class. It is 
thus we are furnished with the requisite names for a 
multitude of new implements, occupations and ideas 
with which we deal in advancing civilization. The 
name physician is derived from the Greek (pvoiKoc, 
natural, and (pvag, nature, so that it properly means 
one who has studied nature, especially the nature of 
the human body. It has become restricted, however, 
to those who use this knowledge for medical purposes, 
and the investigators of natural science have been 
obliged to adopt the new name physicist. The name 
naturalist has been similarly restricted to those who 
study animated nature. The name surgeon originally 
meant handicraftsman, being a corruption of chirurgeon, 
derived from the Greek x u 9 0V 9y^i hand- worker. It 
has long been specialized, however, to those who per- 
form the mechanical parts of the sanatory art. 

Language abounds with other examples. Minister originally 
meant a servant, or one who acted as a minor of another. Now 



THE GROWTH OF LANGUAGE. 51 

it often means specially the most important man in the kingdom. 
A chancellor was a clerk or even a door-keeper who sat in a place 
separated by bars or cancelli in the offices of the Roman em- 
peror's palace ; now it is always the name of a high or even the 
highest dignitary. Peer was an equal (Latin, Par), and we still 
speak of being tried by our peers ; but now, by the strange acci- 
dents of language, it means the few who are superior to the rest 
of the Queen's subjects in rank. Deacon, Bishop, Clerk, Queen, 
Captain, General, are all words which have undergone a like 
process of specialization. In such words as telegraph, rail, 
signal, station, and many words relating to new inventions, we 
may trace the progress of change in a lifetime. 

4. Desynonymization. 

One effect of the process of specialization is very soon 
to create a difference between any two words which 
happen from some reason to be synonymous. Two or 
more words are said to be synonymous (from the Greek 
ovv, with, and ovofia, name) when they have the same 
meaning, as in the case, perhaps, of teacher and in- 
structor, similarity and resemblance, beginning and 
commencement, sameness and identity, hypothesis and 
supposition, intension and comprehension. But the 
fact is that words commonly called synonymous are 
seldom perfectly so, and there are almost always 
shades of difference in meaning or use, which are ex- 
plained in such works as Crabb's English Synonyms. 
A process called by Coleridge desynonymization, and by 
Herbert Spencer differentiation, is always going on, 
which tends to specialize one of a pair of synonymous 
words to one meaning and the other to another. Thus 
wave and billow originally meant exactly the same 
physical effect, but poets have now appropriated the 
word " billow," whereas wave is used chiefly in practical 



52 TERMS. 

and scientific matters. Undulation is a third synonym, 
which will probably become the sole scientific term for 
a wave in course of time. Cab was originally a mere 
abbreviation of cabriolet, and therefore of similar mean- 
ing, but it is now specialized to mean almost exclusively 
a hackney cab. In America car is becoming restricted 
to the meaning of a railway car. 

It may be remarked that to possess a great number of syn- 
onymous terms is a logical defect in a language, since we 
acquire the habit of using them indifferently without being sure 
that they are not subject to ambiguities and obscure differences 
of meaning. The English language is especially subject to the 
inconvenience of having a complete series of words derived from 
Greek or Latin roots nearly synonymous with other words of 
Saxon or French origin. The same statement may, in fact, be 
put into Saxon or classical English ; and we often, as Whately 
has well remarked, seem to prove a statement by merely repro- 
ducing it in altered language. The rhetorical power of the 
language may be increased by the copiousness and variety of 
diction, but pitfalls are thus prepared for all kinds of fallacies. 

5. Metaphorical Extension of Meaning. 

In addition to the effects of generalization and speci- 
alization, vast additions and changes are made in lan- 
guage by the process of metaphorical extension of the 
meaning of words. This change may be said, no doubt, 
to consist in generalization, since there must always be 
a resemblance between the new and old applications of 
the term. But the resemblance is often one of a most 
distant and obscure kind, such as we should call analogy 
rather than identity. All words used metaphorically, 
or as similitudes, are cases of this process of extension. 
The name metaphor is derived from the Greek words 



THE GKOWTH OF LANGUAGE. 53 

Herd, over, and (pzpeiv, to carry ; and expresses appar- 
ently the transference of a word from its ordinary to a 
peculiar purpose. Thus the old similitude of a ruler to 
the pilot of a vessel gives rise to many metaphors, as in 
speaking of the prime minister being at the helm of 
the state. The word governor, and all its derivatives, 
is, in fact, one result of this metaphor, being merely a 
corrupt form of gubernator, steersman. 

The words compass, polestar, ensign, anchor, and many others 
connected with navigation, are constantly used in a metaphorical 
manner. From the use of horses and hunting we derive another 
set of metaphors ; as, in taking the reins of government, over- 
turning the government, taking the bit between the teeth, the 
government whip, being heavily weighted, etc. No doubt it 
might be shown that every other important occupation of life has 
furnished its corresponding stock of metaphors. 

6. Origin of the Mental Vocabulary. 

This process, besides going on consciously at the 
present day, must have acted throughout the history of 
language, and we owe to it almost all, or probably all, 
the words expressive of refined mental or spiritual ideas. 
The very word spirit, now the most refined and imma- 
terial of ideas, is but the Latin spiritus, a gentle breeze 
or breathing ; and inspiration, esprit, or wit, and many 
other words, are due to this metaphor. It is truly 
curious, however, that almost all the words in different 
languages denoting mind or soul imply the same 
analogy to breath. Thus, soul is from the Gothic root 
denoting a strong wind or storm ; the Latin words 
animus and anima are supposed to be connected with 
the Greek ave[j,og, wind ; ^v%i\ is certainly derived from 



54 TERMS. 

tpvxu, to blow ; irvevjia, air or breath, is used in the 
New Testament for Spiritual Being; and our word 
ghost has a similar origin. 

Almost all the terms employed in mental philosophy or 
metaphysics, to denote actions or phenomena of mind, are ulti- 
mately derived from metaphors. Apprehension is the putting 
forward of the hand to take anything ; comprehension is the 
taking of things together in a handful ; extension is the spread- 
ing out ; intention, the bending to ; explication, the unfolding ; 
application, the folding to ; conception, the taking up together ; 
relation, the carrying back ; experience is the thoroughly going 
through a thing ; difference is the carrying apart ; deliberation, 
the weighing out ; interruption, the breaking between ; proposi- 
tion, the placing before ; intuition, the seeing into ; and the list 
might be almost indefinitely extended. Our English name for 
reason, the understanding, obviously contains some physical 
metaphor which has not been fully explained ; with the Latin 
intellect there is also a metaphor; 

Every sense gives rise to words of refined meaning ; sapience, 
taste, insipidity, gout, are derived from the sense of taste ; saga- 
city, from the dog's extraordinary power of smell ; but as the 
sense of sight is by far the most acute and intellectual, it gives 
rise to the larger part of language ; clearness, lucidity, obscurity, 
haziness, perspicuity, and innumerable other expressions, are 
derived from this sense. 

7. The Fertility of Root-words. 

It is trnly astonishing to notice the power which 
language possesses by the processes of generalization, 
specialization, and metaphor, to create many words 
from one single root. Prof. Max Muller has given a 
remarkable instance of this in the case of the root 
spec, which means sight, and appears in the Aryan lan- 
guages, as in the Sanscrit spas, the Greek oicenTOfiai, 



THE GKOWTH OF LANGUAGE. 55 

with transposition of consonants, in the Latin specio, 
and even in the English spy. 

The following is an incomplete list of the words developed 
from this one root ; species, special, especial, specimen, spice, 
spicy, specious, speciality, specific, specialization, specie (gold, or 
silver), spectre, specification, spectacle, spectator, spectral, spec- 
trum, speculum, specular, speculation. The same root also enters 
into composition with various prefixes ; and we thus obtain a 
series of words, suspect, aspect, circumspect, expect, inspect, 
prospect, respect, retrospect, introspection, conspicuous, perspi- 
cuity, perspective ; with each of which, again, a number of de- 
rivatives is connected. Thus, from suspect, we derive suspicion, 
suspicable, suspicious, suspiciously, suspiciousness. I have esti- 
mated that there are in all at least 246 words, employed at some 
period or other in the English language, which undoubtedly 
come from the one root spec. 

J. S. Mill's Logic, Book IV, Chap. V, " On the Natural History 

of the Variations in the Meanings of Terms." 
Archbishop Trench, On the Study of Words. 
Max Miiller, Lectures on the Science of Language. 
Whitney's Life and Growth of Language. 

In this section, on "The Growth of Lan- 
guage," we have considered:— 

1. The Tivo Principal Processes of Growth. 

2. Generalization, 

3. Specialization. 

4. Desynonymization. 

5. Metaphorical Extension of Meaning* 

6. Origin of the Mental Vocabulary. 

7. The Fertility of Root-words, 



56 TERMS. 



SECTION Y- 

THE PERFECT AND THE IMPERFECT 
KNOWLEDGE OF TERMS. 

1. Statement of the Question. 

In treating of Terms it is necessary that we should 
clearly understand what a perfect notion of the mean- 
ing of a term requires. When a name such as monarch, 
or civilization, or autonomy is used, it refers the mind 
to some thing or some idea, and we ought, if possible, 
to obtain a perfect knowledge of the thing or idea be- 
fore we use the word. In what does this perfect knowl- 
edge consist ? What are its necessary characters ? 

This is a question which the celebrated mathematician and 
philosopher Leibnitz attempted to answer in a small treatise or 
tract first published in the year 1684. This tract has been the 
basis of what is given on the subject in several recent works 
on Logic, and a complete translation of the tract has been 
appended by Mr. Baynes to his translation of the Port Royal 
Logic. As the remarks of Leibnitz himself are not always easy 
to understand, I will not confine myself to his exact words, but 
will endeavor to give the simplest possible statement of his views, 
according as they have been interpreted by Dr. Thomson or Sir 
W. Hamilton. 

2. Scheme of Distinctions. 

Knowledge is either obscure or clear; either con- 
fused or distinct ; either adequate or inadequate ; and 
lastly, either symbolical or intuitive. Perfect knowledge 
must be clear, distinct, adequate and intuitive ; if it 



KNOWLEDGE OF TERMS. 57 

fails in any of these respects it is more or less imper- 
fect. Wo may, therefore, classify knowledge as in the 
following scheme : — 

Knowledge 



Clear Obscun 


Distinct 


Confused 


Adequate 


Inadequate 


Intuitive 
Perfect. 


Symbolical 
Imperfect. 



(1) Clear and Obscure Knowledge Distinguished. — 

A notion, that is to say our knowledge of a thing, 
is obscure when it does not enable us to recognize 
the thing again and discriminate it from all other 
things. We have a clear notion of a rose and of most 
common flowers because we can recognize them with 
certainty, and do not confuse them with each other. 
Also we have a clear notion of any of our intimate 
friends or persons whom we habitually meet, because 
we recognize them whenever we see 'them with the 
utmost certainty and without hesitation. 

It is said that a shepherd acquires by practice a clear notion of 
each sheep of his flock, so as to enable him to single out any one 
separately, and a keeper of hounds learns the name and character 
of each hound, while other persons have only an obscure idea of 
the hounds generally, and could not discriminate one from the 
other. But the geologist cannot give a clear idea of what sand- 
stone, conglomerate, or schist, or slate, or trap rock consists, be- 
cause different rocks vary infinitely in degree and character, and 
it is often barely possible to say whether a rock is sandstone or 



58 TERMS. 

conglomerate, schist or slate, and so on. In the lower forms of 
life the naturalist hardly has a clear notion of animal life, as dis- 
tinguished from vegetable life ; it is often difficult to decide 
whether a protophyte should be classed with animals or plants. 

(2) Distinct and Confused Knowledge Distinguished. 

— Clear knowledge, again, is confused, when we cannot 
distinguish the parts and qualities of the thing known, 
and can only recognize it as a whole. Though any one 
instantly knows a friend, and could discriminate him 
from all other persons, yet he would generally find it 
impossible to say how he knows him, or by what 
marks. He could not describe his figure or features, 
but in the very roughest manner. A person unpractised 
in drawing, who attempts to delineate even such a 
familiar object as a horse or cow, soon finds that he has 
but a confused notion of its form, while an artist has a 
distinct idea of the form of every limb. The chemist 
has a distinct as well as a clear notion of gold and silver, 
for he can not only tell with certainty whether any 
metal is really gold or silver, but he can specify and 
describe exactly the qualities by w T hich he knows it; 
and could, if necessary, mention a great many other 
qualities as well. 

We have a very distinct notion of a chess-board, because 
we know it consists of 64 square spaces ; and all our ideas of 
geometrical figures, such as triangles, circles, parallelograms, 
squares, pentagons, hexagons, etc., are or ought to be perfectly 
distinct. But when we talk of a constitutional government, or a 
civilized nation, we have only the vaguest idea of what we mean. 
We cannot say exactly what is requisite to make a government 
constitutional, without including also governments which we do 
not intend to include ; and so of civilized nations ; these terms 
have neither distinct nor clear meanings. 



KNOWLEDGE OF TERMS. 59 

It is to be remarked that no simple idea, such as that of red 
color, can be distinct in the meaning here intended, because r.o- 
body can analyze red color, or describe to another person what 
it is. A person who has been blind from birth cannot be made 
to conceive it ; and it is only by bringing an actual red object 
before the eye that we can define its character. The same is 
generally true of all simple sensations, whether tastes, smells, 
colors, or sounds ; these, then, may be clearly known, but not 
distinctly, in the meaning which Leibnitz gives to this word. 



(3) Adequate and Inadequate Knowledge Distin- 
guished. — To explain the difference which Leibnitz 
intended to denote by the names adequate and inade- 
quate, is not easy. He says, " When everything which 
enters into a distinct notion is distinctly known, or 
when the last analysis is reached, the knowledge is 
adequate, of which I scarcely know whether a perfect 
example can be offered — the knowledge of numbers, 
however, approaches near to it." 

To have adequate knowledge of things, then, we 
must not only distinguish the parts which make up 
our notion of a thing, but the parts which make up 
those parts. For instance, we might be said to have 
an adequate notion of a chess-board, because we know 
it to be made up of 64 squares, and we know each 
of those squares distinctly, because each is made 
up of 4 equal right lines, joined at right angles. 
Nevertheless, we cannot be said to have a distinct 
notion of a straight line, because we cannot well 
define it, or resolve it into anything simpler. To 
be completely adequate, our knowledge ought to ad- 
mit of analysis after analysis ad infinitum, so that 
adequate knowledge would be impossible. But, as Dr. 



60 TERMS. 

Thomson remarks, we may consider any knowledge 
adequate which carries the analysis sufficiently far i'or 
the purpose in view. 

A mechanist, for instance, has adequate knowledge of a 
machine, if he not only knows its several wheels and parts, but 
the purposes, materials, forms, and actions of those parts ; pro- 
vided, again, that he knows all the mechanical properties of 
the materials, and the geometrical properties of the forms which 
may influence the working of the machine. But he is not ex- 
pected to go on still further and explain why iron or wood of a 
particular quality is strong or brittle, why oil acts as a lubricator, 
or on what axioms the principles of mechanical forces are 
founded. 

(4) Intuitive and Symbolical Knowledge Distin- 
guished. — Lastly, we must notice the very important 
distinction of symbolical and intuitive knowledge. 
From the original meaning of the word, intuitive 
would denote that which we gain by seeing (Latin, 
intueor, to look at), and any knowledge which we have 
directly through the senses, or by immediate communi- 
cation to the mind, is called intuitive. Thus we may 
learn intuitively what a square or a hexagon is, but 
hardly what a chiliagon or figure of 1000 sides is. 

We could not tell the difference by sight of a figure 
of 1000 sides and a figure of 1001 sides. Nor can we 
imagine any such figure completely before the mind. 
It is known to us only by name or symbolically. 
All large numbers, such as those which state the 
velocity of light (186,000 miles per second), the dis- 
tance of the sun (91,000,000 miles), and the like, are 
known to us only by symbols, and they are beyond our 
powers of imagination. 



KNOWLEDGE OF TERMS. 61 

In arithmetic and algebra we are chiefly occupied 
with symbolical knowledge only, since it is not neces- 
sary in working a long arithmetical question or an alge- 
braical problem that we should realize to ourselves at 
each step the meaning of the numbers and symbols. 
We learn from algebra that if we multiply together the 
sum and difference of two quantities we get the differ- 
ence of the squares ; as in symbols 

(a 4- b) {a - b) = a? - W ; 

which is readily seen to be true, as follows : 

a + b 
a — b 
a 2 + ab 

— ab-W - 
a? _j_ o — #>. 

In the above we act darkly or symbolically, using the 
letters a and b according to certain fixed rules, without 
knowing or caring what they mean; and whatever 
meaning we afterwards give to a and b we may be sure 
the process holds good, and that the conclusion is true 
without going over the steps again. 

But in geometry, we argue by intuitive perception of 
the truth of each step, because we actually employ a 
representation in the mind of the figures in question, 
and satisfy ourselves that the requisite properties are 
really possessed by the figures. Thus the algebraical 
truth shown above in symbols may be easily proved to 
hold true of lines and rectangles contained under those 
lines, as a corollary of the 5th Prop, of Euclid's Second 
Book. 



62 TERMS. 

3. The Intuitive and Symbolic Methods Com- 
pared. 

Much might be said concerning the comparative ad- 
vantages of the intuitive and symbolical methods. The 
latter is usually much the less laborious, and gives the 
most Avidely applicable answers; but the symbolical 
seldom or never gives the same command and compre- 
hension of the subject as the intuitive method. Hence 
the study of geometry is always indispensable in educa- 
tion, although the same truths are often more readily 
proved by algebra. It is the peculiar glory of Newton 
that he was able to explain the motions of the heavenly 
bodies by the geometric or intuitive method; whereas 
the greatest of his successors, such as Lagrange or 
Laplace, have treated these motions by the aid of 
symbols. 

What is true of mathematical subjects may be ap- 
plied to all kinds of reasoning ; for words ape symbols 
as much as A, B, C, or x, y, z, and it is possible to 
argue with words without any consciousness of their 
meaning. Thus if I say that "selenium is a dyad 
element, and a dyad element is one capable of replacing 
two equivalents of hydrogen," no one ignorant of 
chemistry will be able to attach any meaning to these 
terms, and yet any one will be able to conclude that 
"selenium is capable of replacing two equivalents of 
hydrogen." Such a person argues in a purely symboli- 
cal manner. Similarly, whenever in common life we 
use words, without having in mind at the moment the 
full and precise meaning of the words, we possess sym- 
bolical knowledge only. 






KNOWLEDGE OF TERMS. 63 

There is no worse habit for a student or reader to acquire 
than that of accepting words instead of a knowledge of things. 

It is perhaps worse than useless to read a work on natural history 
about Infusoria, Foraminifera, Rotifera and the like, if these 
names do not convey clear images to the mind. Nor can a 
student who has not witnessed experiments, and examined the 
substances with his own eyes, derive any considerable advantage 
from works on chemistry and natural philosophy, where he will 
meet with hundreds of new terms which would be to him mere 
empty and confusing signs. On this account we should lose no 
opportunity of acquainting ourselves, by means of our senses, 
with the forms, properties and changes of things, in order that 
the language we employ may, as far as possible, be employed 
intuitively, and we may be saved from the absurdities and falla- 
cies into which we might otherwise fall. We should observe, in 
short, the advice of Bacon — Ipsis consueseere rebus — to accustom 
ourselves to things themselves. 

Hamilton's Lectures on Logic, Lect. IX. 

Baynes' Port Royal Logic. Part I, Chap. IX, and Appendix. 

In this section, on " The Perfect and the Im- 
perfect Knowledge of Terms," we have con- 
sidered :— 

1. The Statement of the Question. 

2. The Scheme of Distinctions. 

3. The Intuitive and Symbolic Methods Com- 

pared. 



CHAPTER IU 

PROPOSITIONS. 

The treatment of Propositions will involve a con- 
sideration of the following topics : (1) The Kinds 
of Propositions ; (2) The Opposition of 
Propositions ; (3) Conversion and Imme- 
diate Inference ; and (4) The logical Anal- 
ysis of Sentences. These topics will be treated in 
separate sections. 



SECTION !♦ 

THE KINDS OF PROPOSITIONS. 

1. Meaning of " Proposition " Explained. 

A term standing alone is not capable of expressing 
truth ; it merely refers the mind to some object or 
class of objects, about which something may be affirmed 
or denied, but about which the term itself does not 
affirm or deny anything. "Sun," "air," "table," 
suggest to every mind objects of thought, but we can- 
not say that "sun is true," or "air is mistaken," or 
"table is false." "We must join words or terms into 
sentences or propositions before they can express those 
reasoning actions of the mind to which truth or falsity 
maybe attributed. "The sun is bright," "the air is 
fresh," " the table is unsteady," are statements which 
may be true or may be false, but we can certainly 
entertain the question of their truth in any circum- 
stances. Now as the logical term was defined to be 



KINDS OF PKOPOSITIONS. 65 

any combination of words expressing an act of simple 
apprehension, so a logical proposition is any combina- 
tion of words expressing an act of judgment. The 
proposition is, in short, the result of an act of judg- 
ment reduced to the form of language. 

What the logician calls a proposition the grammarian calls a 
sentence. But though every proposition is a sentence, it is not 
to be supposed that every sentence is a proposition. There are 
in fact several kinds of sentences more or less distinct from a 
proposition, such as a Sentence Iuterrogative or Question, a Sen- 
tence Imperative or a Command, a Sentence Optative, which ex- 
presses a wish, and an Exclamatory Sentence, which expresses 
an emotion of wonder or surprise. These kinds of sentence 
may possibly be reduced, by a more or less indirect mode of 
expression, to the form of a Sentence Indicative, which is the 
grammatical name for a proposition ; but until this be done they 
have no proper place in Logic, or at least no place which logicians 
have hitherto sufficiently explained. 

2. Analysis of a Proposition. 

The name proposition is derived from the Latin 
words pro, before, and pono, I place, and means the 
laying or placing before any person the result of an act 
of judgment. Now every act of judgment or compari- 
son must involve the two things brought into compari- 
son, and every proposition will naturally consist of three 
parts — the two terms, or names, denoting the things 
compared, and the copula, or verb, indicating the con- 
nection between them, as it was ascertained in the act 
of judgment. Thus the proposition, " Gold is a yellow 
substance," expresses an agreement between gold and 
certain other substances previously called yellow in re- 
gard to their color. Gold and yellow substance are 
evidently the two terms, and is the copula. 



66 PEOPOSITIONS*. 

It is always usual to call the first term of a proposi- 
tion the subject^ since it denotes the underlying matter, 
as it were (Latin, sub, under, and jactum, laid) about 
which something is asserted. The second term is 
called the predicate, which simply means that which is 
affirmed or asserted. 

This name is derived from the Latin prcedtcare, to assert, 
whence comes the French name predicateur, corrupted into our 
preacher. This Latin verb is not to be confused with the some- 
what similar one predicere, which has the entirely different 
meaning to predict or foretell. I much suspect that newspaper 
writers and others, who pedantically use the verb " to predicate," 
sometimes fall into this confusion, and really mean to predict, but 
it is in any case desirable that a purely technical term like predi- 
cate should not be needlessly introduced into common language, 
when there are so many other good words which might be used. 
This and all other technical scientific terms should be kept to 
their proper scientific use, and the neglect of this rule injures at 
once the language of common life and the language of science. 

3. Categorical and Conditional Propositions. 

Propositions are distinguished into two kinds, accord- 
ing as they make a statement conditionally or uncondi- 
tionally. Thus the proposition, "If metals are heated 
they are softened," is conditional, since it does not 
make an assertion concerning metals generally, but 
only in the circumstances when they become heated. 
Any circumstance which must be granted or supposed 
before the assertion becomes applicable is a condition. 
Conditional propositions are of two kinds, Hypothetical 
and Disjunctive, but their consideration will be best 
deferred to a subsequent chapter. Unconditional prop- 
ositions are those with which we shall for some time 



i 



KINDS OF PROPOSITIONS. 67 

be solely concerned, and these are usually called Cate- 
gorical propositions, from the Greek verb Kar^yopecj 
(kategoreo, to assert or affirm). 

The following diagram will conveniently represent 
the classification of sentences and propositions as far as 
we have yet proceeded : — 



H 
o 

B 



Indicative = Prop. \ gj$g£ J Hypothetical. 
Interrogative { ^"^"""a^ Disjunctive. 

Imperative 
Optative 
. Exclamatory 



4. The Quality and Quantity of Propositions. 

It is now necessary to consider carefully the several 
kinds of categorical propositions. They are classified 
according to quality and according to quantity. As 
regards quality they are either affirmative or negative ; 
as regards quantity they are either universal or par- 
ticular. 

An affirmative proposition is one which asserts a cer- 
tain agreement between the subject and predicate, so 
that the qualities or attributes of the predicate belong 
to the subject. The proposition, "gold is a yellow 
substance," states such an agreement of gold with other 
yellow substances, that we know it to have the color 
yellow, as well as whatever qualities are implied in the 
name substance. A negative proposition, on the other 
hand, asserts, a difference or discrepancy, so that some 
at least of the qualities of the predicate do not belong 
to the subject. "Gold is not easily fusible" denies that 
the quality of being easily fused belongs to gold. 

Propositions are again divided according to quantity 



68 PBOPOSITIONS. 

into universal and particular propositions. If *the prop- 
osition affirms the predicate to belong to the whole of 
the subject, it is an universal proposition, as in the ex- 
ample "all metals are elements," which affirms that 
the quality of being undecomposable or of being simple 
in nature is true of all metals. But if we say " some 
metals are brittle," the quality of brittleness is affirmed 
only of some indefinite portion of the metals, and there 
is nothing in the proposition to make us sure that any 
certain metal is brittle. This is a particular proposition. 

The name particular being derived from the diminutive of the 
Latin pars would naturally signify a small part, but in logic it 
must be carefully interpreted as signifying any part, from the 
smallest fraction up to nearly tlie whole. Particular propositions 
do not include cases where a predicate is affirmed of the whole or 
of none of the subject, but they include any between these 
limits. We may accordingly count among particular proposi- 
tions all such as the following : — 

A very few metals are less dense than water. 

Most elements are metals. 

Many of. the planets are comparatively small bodies. 

Not a few distinguished men have had distinguished sons. 

The reader must carefully notice the somewhat subtle point 
explained further on, that the particular proposition though as- 
serting the predicate only of a part of the subject, does not deny 
it to be true of the whole. 

5. Aristotle's View of Quantity. 

Aristotle considered that there were altogether four 
kinds of proposition as regards quantity, namely- 
Universal. 






Proposition 



Particular. 

Singular. 

Indefinite. 



KIKDS OF PROPOSITIONS. 69 

The singular proposition is one which has a singular 
term for its subject, as in — 

Socrates was yery wise. 
London is a vast city. 

But we may fairly consider that a singular proposi- 
tion is an universal one; for it clearly refers to the 
whole of the subject, which in this case is a single 
individual thing. 

Indefinite or indesignate propositions are those which 
are devoid of any mark of quantity whatever, so that 
the form of words gives us no mode of judging whether 
the predicate is applicable to the whole or only part of 
the subject. Metals are useful, Comets are subject to 
the law of gravitation, are indefinite propositions. In 
reality, however, such propositions have no distinct 
place in logic at all, and the logician cannot properly 
treat them until the true and precise meaning is made 
apparent. 

The predicate must be true either of the whole or of part of 
the subject, so that the proposition, as it stands, is clearly incom- 
plete ; but if we attempt to remedy this and supply the marks of 
quantity, we overstep the proper boundaries of logic and assume 
ourselves to be acquainted with the subject matter or science of 
which the proposition treats. We may safely take the preceding 
examples to mean " some metals are useful " and " all comets are 
subject to the law of gravitation," but not on logical grounds. 
Hence we may strike out of logic altogether the class of indefinite 
propositions, on the understanding that they must be rendered 
definite before we treat them. In the following sections we shall 
frequently use propositions in the indefinite form as examples, on 
the understanding that where no sign of quantity appears, the 
universal quantity is to be assumed. It is probable that wherever 
a term is used alone, it ought to be interpreted as meaning the 
whole of its class. But however this may be, we need not recog- 



70 PROPOSITIONS. 

nize the indefinite proposition as a distinct kind ; and singular 
propositions having been resolved into universals, there remain 
only the two kinds, Universal and Particular. 

6. Names of the Four Propositions. 

Remembering now that there are two kinds of prop- 
osition as regards quality, and two as regards quantity, 
we shall be able to form altogether four varieties, 
thus : 



Proposition < 



TTnivprsal J Affi ™ative A 

Universal | Negative E 

Particular -I AffirmatiTe ' 

rarticuiai j Negative Q 



The vowel letters placed at the right hand are sym- 
bols or abbreviated names, which are always used to 
denote the four kinds of proposition ; and there will be 
no difficulty in remembering their meaning if we ob- 
serve A and I occur in the Latin verb affirmo, I affirm, 
and E and in nego, I deny. 

There will generally be no difficulty in referring to its proper 
class any proposition that we meet with in writings. The mark 
of universality usually consists of some adjective of quantity, 
such as all, every, each, any, the whole ; but whenever the predi- 
cate is clearly intended to apply to the whole of the subject we 
may treat the proposition as universal. The signs of a particu- 
lar proposition are the adjectives of quantity, some, certain, a few, 
many, most, or such others as clearly indicate part at least. 

The negative proposition is known by the adverbial particle 
not being joined to the copula ; but in the proposition E, that is 
the universal negative, we frequently use the particle no or none 
prefixed to the subject. Thus, "no metals are compound," "none 
of the ancients were acquainted with the laws of motion," are 
familiar forms of the universal negative. 



KINDS OF PROPOSITIONS. 71 

The student must always be prepared too to meet with mis- 
leading or ambiguous forms of expression. Thus the proposition, 
"all the metals are not denser than water," might be taken as E 
or O, according as we interpret it to mean " no metals are denser 
than water," or " not all the metals," etc., the last of course being 
the true sense. The little adjective few is very subject to a subtle 
ambiguity of this kind ; for if I say "few books are at once 
learned and amusing." I may fairly be taken to assert that a few 
books certainly are so, but what I really mean to draw attention 
to is my belief that " the greater number of books are not at once 
learned and amusing." A proposition of this kind is generally 
to be classed rather as O than I. The word some is subject to 
an exactly similar ambiguity between some but not all, and some 
at least, it may be all ; the latter appears to be the correct inter- 
pretation, as shown in the following section (p. 77). 

As propositions are met with in ordinary language they are 
subject to various inversions and changes of the simple logical 
form. 

(1) It is not uncommon, especially in poetry, to find the predi- 
cate placed first, for the sake of emphasis or variety ; as in 
" Blessed are the merciful ;" " Comes something down with even- 
tide ; " " Great is Diana of the Ephesians." There is usually no 
difficulty in detecting such an inversion of the terms, and the 
sentence must then be reduced to the regular order before being 
treated in logic. 

(2) The subject may sometimes be mistaken for the predicate 
when it is described a relative clause, standing at the end of the 
sentence, as in " no one is free who is enslaved by his appetites." 
Here free is evidently the predicate, although it stands in the 
middle of the sentence, and "one who is enslaved by his appe- 
tites " is the real subject. This proposition is evidently of the 
form E. 

7. Variations from the Logical Form, 

Propositions are also expressed in various modes 
differing from the simple logical order, and some of the 
different kinds which arise must be noticed. 



72 PEO POSITIONS. 

(1) Exclusive propositions contain some words, such 
as only, alone, none hut, which limit the predicate to 
the subject. Thus, in " elements alone are metals/' we 
are informed that the predicate "metal" cannot be 
applied to anything except " elements," but we are not 
to understand that "all elements are metals." The 
same meaning is expressed by " none but elements are 
metals;" or, again, by "all that are not elements are 
not metals ; " and this we shall see in the next lesson is 
really equivalent to " all metals are elements." Argu- 
ments which appear fallacious at first sight will often 
be found correct when they contain exclusive proposi- 
tions and these are properly interpreted. 

(2) Exceptive propositions affirm a predicate of all 
the subject with the exception of certain defined cases, 
to which, as is implied, the predicate does not belong. 
Thus, " all the planets, except Venus and Mercury, are 
beyond the earth's orbit," is a proposition evidently 
equivalent to two, viz., that Venus and Mercury are 
not beyond the earth's orbit, but that the rest are. If 
the exceptions are not actually specified by name an 
exceptive proposition must often be treated as a partic- 
ular one. For if I say "all the planets in our system 
except one agree with Bode's law." and do not give the 
name of that one exception, the reader cannot, on the 
ground of the proposition, assert of any planet positively 
that it does agree with Bode's law. 

(3) Explicative op essential propositions are so called 
because they merely affirm of their subject a predicate 
which is known to belong to it by all who can define 
the subject. Such propositions merely unfold what is 
already contained in the subject. "A parallelogram 



KINDS OF PROPOSITIONS. 73 

has four sides and four angles," is an explicative 
or essential proposition. " London, which is the capi- 
tal of England, is the largest city of Europe," contains 
two propositions ; of which one merely directs our at- 
tention to a fact which all may be supposed to know, 
viz., that London is the capital of England. 

(4) Ampliative propositions, on the other hand, join 
a new predicate to the subject. Thus to those who do 
not know the comparative sizes of cities in Europe, the 
last example contains an ampliative proposition. The 
greater number of propositions are of this kind. 

(5) Tautologous or Truistic propositions are those 
which merely affirm the subject of itself, and give no 
information whatever ; as in, "whatever is, is;" "what 
I have written, I have written." 

It is no part of formal Logic to teach us how to interpret the 
meanings of sentences as we meet them in writings ; this is 
rather the work of the grammarian and philologist. Logic treats 
of the relations of the different propositions, and the inferences 
which can be drawn from them ; but it is nevertheless desirable 
that the reader should acquire some familiarity with the real 
logical meaning of conventional or peculiar forms of expression, 
and a number of examples will be found at the end of the book, 
which the learner is requested to classify and treat as directed. 

8. The Modality of Propositions. 

In addition to the distinctions already noticed it has 
long been usual to distinguish propositions as they are 
pure or modal. The pure proposition simply asserts 
that the predicate does or does not belong to the sub- 
ject, while the modal proposition states this cum modo, 
or with an intimation of the mode or manner in which 
the predicate belongs to the subject. The presence of 
4 



74 PROPOSITIONS. 

any adverb of time, place, manner, degree, etc., or any 
expression equivalent to an adverb, confers modality on 
a proposition. " Error is always in haste ; " " justice is 
ever equal; "a perfect man ought always to be con- 
quering himself," are examples of modal propositions 
in this acceptation of the name. 

Other logicians, however, have adopted a different view, and 
treat modality as consisting in the degree of certainty or pro- 
bability with which a judgment is made and asserted. Thus, 
we may say, " an equilateral triangle is necessarily equiangular ; " 
" men are generally trustworthy; " " a falling barometer probably 
indicates a coming storm ; " "Aristotle's lost treatises may possibly 
be recovered ; " and all these assertions are made with a different 
degree of certainty or modality. Dr. Thomson is no doubt right 
in holding that the modality does not affect the copula of the 
proposition, and the subject could only be properly treated in a 
work on Probable Reasoning. 

Many logicians have also divided propositions according as they 
are true or false, and it might well seem to be a distinction of 
importance. Nevertheless, it is wholly beyond the province of 
the logician to consider whether a proposition is true or not 
in itself ; all that he has to determine is the comparative truth 
of propositions — that is, whether one proposition is true when 
another is. Strictly speaking, logic has nothing to do with a 
proposition by itself; it is only in converting or transmuting 
certain propositions into certain others that the work of reason- 
ing consists, and the truth of the conclusion is only so far in 
question as it follows from the truth of Avhat we shall call the 
premises. It is the duty of the special sciences each in its own 
sphere to determine what are true propositions and what are 
false, and logic would be but another name for the whole of 
knowledge could it take this duty on itself. 

See Mr. Mill's System of Logic, Book I, Chap. IV, which gener- 
ally agrees with what is given above. Chapters V and VI 
contain Mr. Mill's views on the Nature and Import of Prop- 



OPPOSITION OP PROPOSITIONS EXPLAINED. 75 

ositions, which subject may be further studied in Mr. Mill's 
Examination of Sir W. Hamilton's Philosophy, Chap. XVIII ; 
Hamilton's Lectures on Logic, No. XIII ; and Mansel's Pro- 
legomena Logica, Chap. II ; but the subject is too metaphy- 
sical in character to be treated in this work. 

In this Section, on "The Kinds of Propositions," 
we have considered:— 

1. The Meaning of the Word (i Proposition," 

2. The Analysis of a Proposition, 

3. The Categorical and Conditional Propositions, 

4. The Quality and Quantity of Propositions. 

5. Aristotle's View of Quantity, 

6. Karnes of the Four Propositions. 

7 . Variations from the Logical Form, 

8. The Modality of Propositions. 



SECTION II. 
THE OPPOSITION OF PROPOSITIONS. 

1. The Four Propositions Explained. 

We have ascertained that four distinct kinds of prop- 
ositions are recognized by logicians, — the Universal 
affirmative, the Particular affirmative, the Universal 
negative, and the Particular negative, commonly indi- 
cated by the symbols A, E, I, 0. It is now desirable to 
compare together somewhat minutely the meaning and 
use of propositions of these various kinds, so that we 
may clearly learn how the truth of one will affect the 
truth of others, or how the same truth may be thrown 
into various forms of expression. 



76 PROPOSITION'S. 

(1) The universal affirmative proposition A expresses 
the fact that the thing or class of things denoted by the 
subject is included in, and forms part of the class of 
things denoted by the predicate. Thus " all metals are 
elements " means that metals form a part of the class of 
elements, but not the whole. As there are altogether 63 
known elements, of which 48 are metals, we cannot say 
that all elements are metals. The proposition itself 
does not tell us anything about elements in general ; it 
is not, in fact, concerned with elements, metals being 
the subject about which it gives us information. This 
is best indicated by a kind of diagram, first used by the 
celebrated mathematician Euler, in his letters to a 
German princess. In Fig. 1, the metals are supposed 

Fig. 1. 




to be enclosed in the small circle somewhat as sheep 
might be in a pinfold, this circle containing all the 
metals and nothing else. The greater circle is sup- 
posed to contain in a similar manner all the elements 
and nothing else. Now as the small circle is wholly 
within the larger one, it follows that all the metals 
must be counted as elements, but of the part of the 
elements outside the circle of metals we know nothing 
from the proposition. 

(2) The particular affirmative proposition I exactly 



OPPOSITION OF PROPOSITIONS EXPLAINED. 77 

resembles A in meaning, except that only part of the 
subject is brought into question. When I say that 
' ' some metals are brittle," I mean that of a collection of 
all the different metals a few at least might be picked 
out which would be found to be brittle ; but the word 
some is exceedingly indefinite, showing neither the 
exact number of brittle metals, nor how we are to 
know them from the others, unless indeed by trying 
whether they are brittle. This proposition will be 
properly represented in Euler's mode by two intersect- 
ing circles, one supposed to enclose all metals, and the 
other all brittle substances. The mere fact of the two 

Fig. 2. 




circles intersecting proves that some part of one class 
must coincide with some part of the other class, which 
is what the proposition is intended to express. Con- 
cerning the portions of the circles which do not overlap, 
the proposition tells us nothing. 

(3) The universal negative proposition E denies the 
existence of any agreement or coincidence between the 
subject and predicate. Thus from " no metals are com- 
pound substances," we learn that no metal is to be 
found among compound substances, and it follows 
necessarily that no compound substance can be found 
among the metals. For were there a compound sub- 



78 PROPOSITIONS. 

stance among the metals, there would evidently be one 
metal at least among the compound substances. This 
entire separation in thought of the two classes is well 
shown in Euler's method by two disconnected circles. 

Fig. 3. 




(4) The particular negative proposition excludes a 
part of the subject from the predicate. When I say 
some metals are not brittle, I intentionally refer only to 
a part of the metals, and exclude them from the class 
of brittle substances ; but I cannot help at the same 
time referring to the whole of the brittle substances. 
If the metals in question coincided with any part of 
the brittle substances they could not be said to be 
excluded from the class. To exclude a thing from any 
space, as from a particular chamber of a house, it must 
not merely be removed from some part, but from any 
part, or from the whole of that space or chamber. 
Euler's diagram for this proposition may be constructed 
in the same manner as for the proposition I as follows : 

Fig. 4. 




It is apparent that though part of the metals fall into 



OPPOSITION OF PROPOSITION'S EXPLAINED. 79 

the circle of brittle substances, yet the remaining por- 
tion are excluded from any part of the predicate. 

2. The Distribution of Terms. 

The learner will easily see that the proposition E is 
distinguished from A and I, by the fact that it gives us 
some information concerning the whole of the predicate, 
because we learn that none of the objects included in 
the predicate can be found among those included in 
the subject. The affirmative propositions, on the other 
hand, warranted us in holding that the objects denoted 
by the subject, or some particular part of them, were 
included in the predicate, but they give us no warrant 
for saying that any specified part of the predicate is in 
the subject. Because we merely know that a substance 
is an element, we do not learn from the proposition 
" all metals are elements " whether it is metal or not. 
And from the proposition " some metals are brittle," we 
certainly cannot ascertain whether any particular brittle 
substance is a metal. We must seek the information 
from other sources. But from " no metals are com- 
pounds " we learn of any compound substance that it 
is not a metal, as well as of a metal that it is not a 
compound substance. The particular negative O dis- 
tributes its predicate, but not its subject, for in saying 
some metals are not brittle, I exclude some metals from 
the whole class of brittle substances. 

The important difference above explained is expressed 
in technical language by saying that the proposition E 
distributes its predicate, whereas the affirmative proposi- 
tions A and I do not distribute their predicates. By 
distribution of a term is simply meant talcing it univer- 



80 PROPOSITIONS. 

sally 3 or referring to all parts of it ; and as the validity 
of any argument or syllogism will usually depend upon 
the sufficient distribution of the terms occurring in it, 
too much attention cannot be paid to this point. 

Judging from the examples we have had, it will be 
seen that the universal affirmative distributes its sub- 
ject, but not its predicate ; for it gives us some infor- 
mation concerning all metals, but not all elements. The 
particular affirmative distributes neither subject nor 
predicate ; for we do not learn anything from our ex- 
ample concerning all metals nor concerning all brittle 
substances. The universal negative distributes both 
subject and predicate, for we learn something of all 
metals and also of all compound substances. The par- 
ticular negative distributes its predicate, but not its sub- 
ject, for it excludes the subject from the whole of the 
predicate. 

S. Table of Results. 

We may state the results at which we have now 
arrived in the following form : — 

Subject. Predicate. 

TT . , j Affirmative A. Distributed. Undistributed. 

Universal | Negative E> Distributed. Distributed. 



oi 

Q. 
O 

tm 

Q. 



-p .. ■. (Affirmative I. Undistributed. Undistributed. 
Particular } Negative . Undistributed. Distributed. 



4. Relations of the Four Propositions. 

We shall now discover with great ease the relations 
of the four propositions, each to each, that is to say, 
the way in which they are opposed to each other. It 
is obvious that the truth of one proposition interferes 



OPPOSITION" OF PROPOSITIONS EXPLAINED. 81 

more or less completely with the truth of another 
proposition having the same subject and predicate. If 
"all metals are elements," it is impossible that "some 
metals are not elements," and still more palpably im- 
possible, so to say, that "no metals should be elements." 
The proposition A, then, is inconsistent with both E and 
; and, vice versa, E and are inconsistent with A. 
Similarly, E is inconsistent with A and I. But this im- 
portant difference must be noted, that if A be false, 
is necessarily true, but E may or may not be true. If 
it is not true that "all men are sincere," it follows 
that " some men are not sincere," but it does not in 
the least follow that "no men are sincere." This dif- 
ference is expressed by saying that A and are contra- 
dictory propositions, whereas A and E are called con- 
trary propositions. It is plain that A and E, as in " all 
men are sincere" and "no men are sincere," represent 
the utmost possible contrariety of circumstances. In 
order to prove the falsity of A, it is sufficient to estab- 
lish the truth of 0, and it is superfluous, even if pos- 
sible, to prove E ; similarly E is disproved by proving I, 
and it is superfluous to prove A. Any person who 
asserts a universal proposition, either A or E, lays him- 
self under the necessity of explaining away or disprov- 
ing every single exception brought against it. 

An opponent may always restrict himself to the much easier 
task of finding instances which apparently or truly contradict the 
universality of the statement, hut if he takes upon himself to 
affirm the direct contrary, he is himself open to easy attack. 
Were it to be asserted, for instance, that "All Christians are' 
more moral than Pagans," it would be easy to adduce examples 
showing that " Some Christians are not more moral than 
Pagans," but it would be absurd to suppose that it would be 



82 PKOPosmom 

necessary to go to the contrary extreme, and show that "No 
Christians are more moral than Pagans." In short A is suffi- 
ciently and best disproved by 0, and E by I. It will be easily 
apparent that, vice versa, is disproved by A, and I by E ; nor is 
there, indeed, any other mode at all of disproving these particu- 
lar propositions. 



When we compare together the propositions I and 
we find that they are in a certain sense contrary in 
nature, one being affirmative and the other negative, 
but that they are still consistent with each other. It is 
true both that "Some metals are brittle," for instance 
Antimony, Bismuth and Arsenic ; but it is also true 
that "Some metals are not brittle." And the reader 
will observe that when I affirm "Some metals are 
elements," there is nothing in this to prevent the truth 
of "Some metals are not elements," although on other 
grounds we know that this is not true. The proposi- 
tions I and O are called subcontraries each of the other, 
the name connoting a less degree of contrariety than 
exists between A and E. 

As regards the relation of A to I and E to 0, it is 
plain that the truth of the universal includes and 
necessitates the truth of the particular. What may be 
affirmed or denied of all parts of a class may certainly 
be affirmed or denied similarly of some part of the 
class. From the truth of the particular we have no 
right to infer either the truth or falsity of the universal 
of the same quality. These pairs of propositions are 
called subalterns, i. e., one under the other (Latin sub 
under, and alter the other of two), or we may say more 
exactly that I and are respectively the subalter nates 
of A and E, each of which is a subalternans. 



OPPOSITION OF PROPOSITIONS EXPLAINED. 



83 



5. The Scheme of Opposition. 

The relations of the propositions just described are 
all clearly shown in the following scheme: 

A Contraries E 



I 
I 

I 



v#° 



$r 



0° 



%< 
&> % 



?& 



S 

! 

m 



Subcontraries 



6. The Laws of Opposition. 

It is so highly important to apprehend completely 
and readily the consistency or opposition of proposi- 
tions, that I will put the matter in another form. Tak^- 
ing any two propositions having the same subject and 
predicate, they must come under one of the following 
statements : 

1. Of contradictory propositions, one must be true 
and one false. 

2. Of contrary propositions, both cannot be true, 
and both may be false. 

3. Of subcontrary propositions, one only can be false, 
and both may be true. 

4. Of subalterns, the particular is true if the univer- 
sal be true ; but the universal may or may not be true 
when the particular is true. 



84 PROPOSITIONS. 

7. The Conditions of Opposition. 

I put the same matter in yet another form in the 
following table, which shows how the truth of each of 
A, E, I, and 0, affects the truth of each of the others. 





A 


E 


1 







is 


is 


is 


is 


If A be true 


true 


false 


true 


false. 


a c a a 


false 


true 


false 


true. 


it 1 it it 


doubtful 


false 


true 


doubtful 



" " " false doubtful doubtful true. 

It will be evident that from the affirmation of uni- 
versal more information is derived than from the 
affirmation of particulars. It follows that more infor- 
mation can be derived from the denial of particulars 
than from the denial of universals, that is to say, there 
are less cases left doubtful, as in the above table. 

The learner may well be cautioned, however, against an am- 
biguity which has misled some even of the most eminent lo- 
gicians. In particular propositions the adjective some is to be 
carefully interpreted as some, and there may or may not be more 
or all. Were we to interpret it as some, not more nor all, then it 
would really give to the proposition the force of I and com- 
bined. If I say " some men are sincere," I must not be taken as 
implying that "some men are not sincere;" I must be under- 
stood to predicate sincerity of some men, leaving the character of 
the remainder wholly unaffected. It follows from this that, 
when I deny the truth of a particular, I must not be understood 
as implying the truth of the universal of the same quality. To 
deny the truth of " some men are mortal " might seem very 
natural, on the ground that not some but all men are mortal ; but 
then the proposition denied would really be some men are not 
mortal, i. e. not I. Hence when I deny that " some men are 



OPPOSITION TO PROPOSITIONS EXPLAINED. 85 

immortal " I mean that " no men are immortal ; " and wlien I 
deny that " some men are not mortal," I mean that " all men are 
mortal." 

8. The Matter of Propositions. 

It has long been usual to compare propositions as re- 
gards the quality of the subject matter to which they 
refer, and what is technically called the matter was dis- 
tinguished into three kinds, necessary, contingent, and 
impossible. Necessary matter consists of any subject 
in which the proposition A may be affirmed ; impossible 
in which E may be affirmed. Any subject or branch of 
knowledge in which universal statements cannot usually 
be made is called contingent matter, and it implies the 
truth of I and 0. Thus "comets are subject to gravi- 
tation," though an indefinite or indesignate proposition, 
may be interpreted as A, because it refers to a part of 
natural science where such general laws obtain. But 
"men are sincere" would be properly interpreted as 
particular or I, because the matter is clearly contingent. 
The truth of the following statements is evident : 

In necessary matter A and I are true ; E and O false. 

In contingent matter I and are true ; A and E false. 

In impossible matter E and are true ; A and I false. 

In reality, however, this part of logical doctrine is 
thoroughly illogical, because in treating a proposition 
we have no right, as already explained, to assume 
ourselves acquainted with the science to which it re- 
fers. Our duty is to elicit the exact consequences of 
any statements given to us. We must learn in logic to 
transform information in every possible way, but not to 
add extraneous facts. 



36 PROPOSITIONS. 

In this section, on "The Opposition of Proposi- 
tions," we have considered :— 

1. The Explanation of the Four Propositions, 

2. The Distribution of Terms. 

3. The Table of Results. 

4. The Relations of the Four Propositions, 

5. The Scheme of Opposition. 

6. The Laws of Opposition. 

7. The Conditions of Opposition, 

8. The Matter of Propositions. 



SECTION III. 

CONVERSION AND IMMEDIATE INFERENCE. 
1. The Nature of Inference. 

We are said to infer whenever we draw one truth 
from another truth, or pass from one proposition to 
another. As Sir W. Hamilton says, Inference is "the 
carrying out into the last proposition what was virtually 
contained in the antecedent judgments." The true 
sphere of the science of logic indeed is to teach the prin- 
ciples on which this act of inference must be performed, 
and all the previous consideration of terms and propo- 
sitions is only useful or pertinent so far as it assists us 
to understand the processes of inference. We have to 
consider in succession all the modes in which the same 
information may be moulded into different forms of 
expression often implying results of an apparently 
different character. Logicians are not. agreed exactly 
as to what we may include under the name Inference, 
and what we should not. All would allow that there 



CONVEKSION AND INFEBENCE. 87 

is an act of inference when we see drops of water on 
the ground and believe that it has rained. This is a 
somewhat complicated act of inference, which we shall 
consider later under the subject of Induction. Few or 
none would say that there is an act of inference in 
passing from " The Duke of Cambridge is Commander- 
in-chief/' to "The Commander-in-chief is the Duke of 
Cambridge." But without paying much regard to the 
name of the process I shall in this section point out all 
the ways in which we can from a single proposition of 
the forms A, E, I or 0, pass to another proposition. 

2. Conversion of Propositions. 

We are said to convert a proposition when we trans- 
pose its subject and predicate ; but in order that the 
converse or converted proposition shall be inferred from 
the convertend, or that which was to be converted, we 
must observe two rules (1) the quality of the proposi- 
tion (affirmative or negative) must be preserved, and 
(2) no term must be distributed in the Converse unless 
it was distributed in the Convertend. 

(1) Conversion by Limitation.— If in "all metals are 
elements " we were simply to transpose the terms, thus 
— "all elements are metals," we imply a certain knowl- 
edge about all elements, whereas it has been clearly 
shown that the predicate of A is undistributed, and that 
the convertend does not really give us any information 
concerning all elements. All that we can infer is that 
"some elements are metals;" this converse proposi- 
tion agrees with the rule, and the process by which we 
thus pass from A to I is called Conversion by Limitation, 
or Per accidens. 



88 PROPOSITIONS. 

(2) Simple Conversion.— When the converse is a 
proposition of exactly the same form as the convertend 
the process is called simple conversion. Thus from 
"some metals are brittle substances " I can infer "some 
brittle substances are metals," as all the terms are here 
undistributed. Thus I is simply converted into I. 

Again, from "no metals are compounds," I can pass 
directly to " no compounds are metals," because these 
propositions are both in E, and all the terms are there- 
fore distributed. Euler's diagram (p. 73, Fig. 3) clearly 
shows, that if all the metals are separated from all the 
compounds, all the compounds are necessarily separated 
from all the metals. The proposition E is then simply 
converted into E. 

(3) Conversion by Negation. — But in attempting to 
convert the proposition we encounter a peculiar 
difficulty, because its subject is undistributed ; and yet 
the subject should become by conversion the predicate 
of a negative proposition, which distributes its predi- 
cate. Take for example the proposition, " some exist- 
ing things are not material substances." By direct 
conversion this would become "all material substances 
are not existing things;" which is evidently absurd. 
The fallacy arises from existing things being distributed 
in the converse, whereas it is particular in the conver- 
tend ; and the rules of the Aristotelian logic prevent us 
from inserting the sign of particular quantity before 
the predicate. The converse would be equally untrue 
and fallacious were we to make the subject particular, 
as in "some material substances are not existing 
things." We must conclude, then, that the proposi- 
tion cannot be treated either by simple conversion or 



CONVERSIOK AND IHEEKEtfCE. 89 

conversion by limitation. It is requisite to apply a new 
process, which may be called Conversion by Negation, 
and which consists in first changing the convertend 
into an affirmative proposition, and then converting it 
simply. If we attach the negation to the predicate 
instead of to the copula, the proposition becomes "some 
existing things are immaterial substances," and, con- 
verting simply, we have — "some immaterial substances 
are existing things," which may truly be inferred from 
the convertend. The proposition 0, then, is only to 
be converted by this exceptional method of negation. 

(4) Contrapositive Conversion.— Another process of 
conversion can be applied to the proposition A, and is 
known as conversion by contraposition. From "all 
metals are elements," it necessarily follows that " all 
not-elements are not metals." If this be not at the 
first moment apparent, a little reflection will render it 
so, and from Fig. 5 we see that if all the metals be 

Fig. 5. 




among the elements, whatever is not element, or out- 
side the circle of elements, must also be outside the 
circle of metals. 



We may also prove the truth of the contrapositive proposi- 
tion in this way. If what is not-element should be metal, then it 



90 PROPOSITIONS. 

must be an element by the original proposition, or it must be at once 
an element and not an element ; which is impossible according 
to the Primary Laws of Thought (Chap. Ill, Sect. I), since noth- 
ing can both have and not have the same property. It follows 
that what is not-element must be not-metal. 

Mistakes may readily be committed in contrapositive conver- 
sion, from a cause which will be more apparent in Chapter VII. 
We are very liable to infer from a proposition of the form "all 
metals are elements," that all not-metals are not elements, which 
is not only a false statement in itself, but is not in the least 
warranted by the original proposition. In Fig. 5, it is apparent 
that because a thing lies outside the circle of metals, it does not 
necessarily lie outside the circle of elements, which is wider than 
that of metals. Nevertheless the mistake is often made in com- 
mon life ; and the learner will do well to remember that the pro- 
cess of conversion by contraposition consists only in taking the 
negative of the predicate of the proposition A, as a new subject, 
and affirming of it universally the negative of the old subject. 

Contrapositive conversion cannot be applied to the particu- 
lar propositions I and at all, nor to the proposition E, in that 
form ; but we may change E into A by attaching the negation to 
the predicate, and then the process can be applied. Thus " no 
men are perfect," may be changed into "all men are not per- 
fect, i. e., "are imperfect," and then we infer by contraposition 
"all not-imperfect beings are not-men." But not-imperfect is 
really the same as perfect, so that our new proposition is 
really equivalent to "all perfect beings are not men," or "no 
perfect beings are men," (E) the simple converse of the original 
proposition. 

3. Immediate Inference. 

There remain to be described certain deductions 
which may be drawn from a proposition without con- 
verting its terms. They may be called immediate in- 
ferences, and have been yery clearly described by Arch- 
bishop Thomson. 



CONVERSION AND INFERENCE. 91 

(1) Immediate Inference by Privative Conception 

consists in passing from any affirmative proposition to a 
negative proposition implied in it, or equivalent to it, 
or vice versa, in passing from a negative proposition to 
its corresponding affirmative. 

The following table contains a proposition of each kind changed 
by private conception into an equivalent proposition • 

j A all metals are elements. 

[E no metals are compounds. 

(E no men are perfect. 

"I A all men are imperfect. 

j I some men are trustworthy. 

\ some men are not untrustworthy. 

( some men are not trustworthy. 

1 1 some men are untrustworthy. 

The truth of any of the above can be clearly illustrated by 
diagrams ; thus it will be apparent that if the whole circle of 
metals lies inside the circle of elements, no part can lie outside 
of that circle or among the compounds. Any of the above prop- 
ositions may be converted, but the results will generally be such 
as we have already obtained. Thus the simple converse of " no 
metals are compounds" is "no compounds are metals," or "no 
not-elements are metals," the contrapositive of "all metals are 
elements." From the last example we get also by simple con- 
version, " some untrustworthy beings are men," which is obvi- 
ously the converse by negation, as before explained. Applying 
this kind of conversion to "some men are not untrustworthy," 
we have " some not-untrustworthy beings are men." Lastly, 
from " all men are imperfect " we may obtain through conversion 
by limitation, " some imperfect beings are men." 

(2) Immediate Inference by Added Determinants 

consists in joining some adjective or similar qualifica- 
tion both to the subject and predicate of a proposition, 
so as to render the meaning of each term narrower or 
better determined. Provided that no other alteration 



92 PROPOSITIONS. 

is made, the truth of the new proposition necessarily 
follows from the truth of the original in almost all 
cases. 

From " all metals are elements," we may thus infer that " all 
very heavy metals are very heavy elements." From " a comet is 
a material body " we infer " a visible comet is a visible material 
body." But if we apply this kind of inference too boldly we 
may meet with fallacious and absurd results. Thus, from " all 
kings are men," we might infer "all incompetent kings are 
incompetent men ; " but it does not at all follow that those who 
are incompetent as kings would be incompetent in other posi- 
tions. In this case and many others the qualifying adjective is 
liable to bear different meanings in the subject and predicate ; 
but the inference will only be true of necessity when the mean- 
ing is exactly the same in each case, With comparative terms 
this kind of inference will seldom be applicable; thus from "a 
cottage is a building," we cannot infer "a huge cottage is a huge 
building," since a cottage may be large when compared with 
other cottages, but not with buildings generally. 

(3) Immediate Inference by Complex Conception is 

closely similar to the last, and consists in employing the 
subject and predicate of a proposition as parts of a 
more complex system. 

From " all metals are elements," I can pass to " a mixture of 
metals is a mixture of elements." From " a horse is a quadruped " 
I infer " the skeleton of a horse is the skeleton of a quadruped." 
But here again the reader must beware of applying the process 
where the new complex conception has a different meaning in 
the subject and predicate. Thus, from " all Protestants are 
Christians," it does not follow that " a majority of Protestants 
are a majority of Christians," nor that " the most excellent of the 
Protestants is the most excellent of the Christians." 

The student is recommended to render himself familiar 
with all the transformations of propositions, or immediate 



ANALYSIS OF SENTENCES. 93 

inferences described in this lesson ; and copious examples are 
furnished for the purpose. It is a good exercise to throw the 
same proposition through a series of changes, so that it comes 
out in its original form at last, and thus proves the truth of all 
the intermediate changes ; but should conversion by limitation 
have been used, the original universal proposition cannot be 
regained, but only the particular proposition corresponding 
to it. 

On Immediate Inference, Archbishop Thomson, Outline of the 
Laws of Thought, Sections 85-92. 

In this section, on " Conversion and Immediate 
Inference," we have considered :— 

1. The Nature of Inference* 

2. Conversion. 

3. Immediate Inference, 



SECTION IY. 

THE LOGICAL ANALYSIS OF SENTENCES. 

1. Relation of Logic to this Topic. 

Propositions as they are usually to be found in 
written or spoken compositions seldom exhibit the 
simple form, the conjunction of a subject, copula, and 
predicate, which we have seen to be the proper logical 
construction. Not only is the copula often confused 
with the predicate, but several propositions may be 
combined into one grammatical sentence. For a full 
account of the analysis of sentences I shall refer to 
several excellent little works devoted to the subject ; 
but I will here attempt to give a sketch of the various 
ways in which a sentence may be constructed. 



94 PROPOSITIONS. 

2. The Grammatical and the Logical Predicate. 

So often is the copula united to the predicate in 
ordinary language, that the grammarian treats the 
proposition as composed of only two parts, the subject 
and predicate, or verb. Thus the proposition, " The sun 
rises," apparently contains nothing but a subject " the 
sun," and a predicate "rises;" but the proposition is 
really equivalent to "the sun is rising," in which the 
copula is distinctly shown. We shall, therefore, con- 
sider the verb or grammatical predicate as containing 
both copula and logical predicate. In Latin one single 
word may combine all the three parts of the proposition, 
as in sum, "lam; " and the celebrated exclamation of 
Caesar, Veni, vidi, vici, "I came, I saw, I conquered," 
contains three distinct and complete propositions in 
three words. These peculiar cases only arise, however, 
from the parts of the proposition having been blended 
together and disguised in one word ; and in the Latin 
sum, the letter m is a relic of the pronoun me, which is 
the real subject of the proposition. If we had a perfect 
acquaintance with the Grammar of any language it 
would probably not contradict the logical view of a 
sentence, but would perhaps explain how the several 
parts of the complete proposition had become blended 
and apparently lost, just as the words will and not are 
blended in the colloquial " I wont." 



3. The Plurality of Propositions in a Sentence. 

A grammatical sentence may contain any number of 
distinct propositions, which admit of being separated 



ANALYSIS OF SENTENCES. 95 

but which are combined together for the sake of 
brevity. In the sentence, 

"Art is long and Time is fleeting," 

there are two distinct subjects, Art and Time, and two 
predicates, "long" and "fleeting," so that we have 
simply two propositions connected by the conjunction 
and. We may have, however, several distinct subjects 
with one and the same predicate ; as in 

" Thirty days hath September, 
April, June, and November." 

In this well-known couplet the predicate "having 
thirty days " is placed first for the sake of emphasis, 
and there are four subjects, September, April, etc., of 
each of which it is affirmed. Hence these lines really 
contain four distinct propositions. 

Again, there may be one subject with a plurality of 
predicates, so that several different propositions are 
asserted without the repetition of the subject and 
copula. Thus the sentence 

"Nitrogen is a colorless, tasteless, inodorous gas, 
slightly lighter than air," contains one subject only, 
Nitrogen, but four or five predicates ; it is plainly 
equivalent to "Nitrogen is colorless," "Nitrogen is 
tasteless," "Nitrogen is a gas," and so on. 

Lastly, we may have several subjects and several 
predicates all combined in the same sentence, and with 
only one copula, so that each predicate is asserted of 
each subject ; and a great number of distinct proposi- 
tions are condensed into one brief sentence. Thus in 
the sentence, " Iron, Copper, Lead and Zinc are abun- 



96 PROPOSITIONS. 

dant, cheap and useful metals," we have evidently four 
subjects, and we may be said to have four predicates, 
"abundant," "cheap," "useful," and "metal." As 
there is nothing to prevent our applying each predicate 
to each subject the sentence really contains 16 distinct 
propositions in only 11 words; thus "Iron is abun- 
dant," " Iron is cheap," " Copper is abundant," " Cop- 
per is cheap," and so on. In the curious sentence : 

" Hearts, tongues, figures, scribes, bards, poets, can- 
not think, speak, cast, write, sing, number, his love to 
Antony,"* Shakspeare has united six subjects and six 
predicates, or verbs, so that there are, strictly speaking, 
six times six or thirty-six propositions. 

In all the cases above noticed the sentence is said to be com- 
pound, and the distinct propositions combined together are said 
to be co-ordinate with each other, that is of the same order or 
kind, because they do not depend upon each other, or in any way 
affect each other's truth. The abundance, cheapness, or utility 
of iron need not be stated in the same sentence with the qualities 
of copper, lead or zinc ; but as the predicates happen to be the 
same, considerable trouble in speaking or writing is saved by 
putting as many subjects as possible to the same set of predi- 
cates. It is truly said that brevity is the soul of wit, and one of 
the great arts of composition consists in condensing as many 
statements as possible into the fewest words, so long as the 
meaning is not confused thereby. 

4. Complex Sentences. 

Propositions are, however, combined in a totally 
different manner when one proposition forms a part of 
the subject or predicate of the other. Thus in the 

* Antony and Cleopatra, Act HE, Sec. 2. 



ANALYSIS OF SENTENCES. 97 

sentence, "The man who is upright need not fear 
accusation," there are two verbs, and two propositions, 
but one of these only describes the subject of the other; 
" who is upright " evidently restricts the application of 
the predicate "need not fear accusation" to a part of 
the class "man." The meaning of the whole sentence 
might be expressed in the form 

"The upright man need not fear accusation." 

And it is clearly seen that the clause or apparent prop- 
osition is substituted for an adjective. Such a clause 
or proposition is called subordinate, because it merely 
assists in the formation of the principal sentence, and 
has no meaning apart from it ; and any sentence con- 
taining a subordinate clause is said to be complex. 
Almost any part of a sentence may thus be replaced by 
a subordinate clause. Thus in " Oxygen and Mtrogen 
are the gases which form the largest part of the at- 
mosphere," there is a subordinate clause making part 
of the predicate, and the meaning might be expressed 
nearly as well in this way, "Oxygen and Nitrogen are 
the gases forming the largest part of the atmosphere." 



In the case of a modal proposition, or one which states the 
manner in which the predicate belongs to the subject, the mode 
may be expressed either by an adverb, or by a subordinate 
clause. " As a man lives so he dies " is. such a proposition ; for 
it means, " a man dies as he lives," and " as he lives" is equiva- 
lent to an adverb ; if he lives well, he dies well ; if he lives 
badly, he dies badly. Adverbs or adverbial clauses may also 
specify the time, place, or any other circumstance concerned in 
the truth of the main proposition. 

Assuming the learner to be acquainted with the grammatical 
5 



98 PROPOSITIONS. 

terms used, we may thus state the parts of which the most 
complex sentence must consist. 

The subject may consist of — 

1. A noun ; as in " The Queen reigns. " 

2. A pronoun ; as in " She reigns." 

3. An adjective converted into a noun ; as in " Whites are 
civilized." 

4. A gerund ; as " Seeing is believing." 

5. An infinitive; as " To see is to believe." 

6. A subordinate clause; as " Who falls from virtue is lost. 
The subject may be qualified or restricted by combining with 

it an attribute which may be expressed in any of the following 
ways: 

1. An adjective ; as " Fresh air is wholesome." 

2. A participle ; as " Falling stars are often seen." 

3. A noun used as an adjective ; as " Iron ships are now much 
employed." 

4. A noun and preposition; as " ships of iron are now much 
employed." 

5. A possessive case ; as " Chatham's son was the great minister 
Pitt." 

6. A noun in apposition; as*' The Metropolis London is the 
most populous of cities." 

7. A gerund or dative infinitive ; as, " The desire to go abroad 
is common in Englishmen." 

The predicate consists almost always of a verb, which often 
has some object or qualifying words ; thus it may be — 

1. A simple tense of a complete verb ; as " The sun rises" 

2. A compound tense ; as " The sun has risen." 

3. An incomplete verb and complement ; as " The sea appears 
rough" 

4. The verb " to be" and an adjective; as "Time is fleeting." 

5. A verb with an object ; as " Warmth melts ice." 

6. A verb with an adverbial ; as " The snow falls thickly." 

The object of a verb is usually a noun or pronoun, but any 
other of the six kinds of expressions which may serve as a sub- 
ject may also serve as an object, 



ANALYSIS OF SENTENCES. 99 

The adverbial qualifying a verb and expressing the manner, 
time, place, or other circumstance affecting the proposition may 
be — 

1. An adverb ; as " The days pass slowly." 

2. A noun and preposition ; as " The resolution was passed by 
a large majority" 

3. An absolute phrase ; as " The snow melts, the sun having 
risen." 

4. A dative infinitive ; as " She stoops to conquer." 

5. Any phrase equivalent to an adverb ; as " The dividends 
are paid twice a year." 

5, Modes of Exhibiting Construction. 

Various modes of exhibiting the construction of sen- 
tences by symbols and names for the several parts have 
been invented ; but I believe that by far the simplest 
and most efficient mode is to exhibit the construction 
in the form of a diagram. Any two or more parts of a 
sentence which are co-ordinate with each other, or bear 
the same relation to any other part, are written along- 
side each other, and coupled together by a bracket; 
thus the diagram, — 



Iron 
Copper 
Lead 
Zinc 



are 



" abundant, 

cheap, 

useful 
^ metals, 

clearly shows that there are four co-ordinate subjects, 
and four co-ordinate predicates in the example pre- 
viously taken. 

Whenever one part of a sentence is subordinate to 
another part it may be connected with it by a line 
drawn in any convenient direction. Thus the analysis 
of the following sentence is readily shown by the dia- 
gram below it : — 



100 PKOPOSITIONS. 

" No one who is a lover of money, a lover of pleasure, 
and a lover of glory, is likewise a lover of mankind ; 
but only he who is a lover of virtue." 

( a lover of money, 
who is < a lover of pleasure, 
( a lover of glory. 

heVnly is \ a loTer of mallkind > 

I 
who is a lover of virtue. 

We see that the sentence is both compound and com- 
plex, that is to say it contains two principal co-ordinate 
propositions with a common predicate, "a lover of 
mankind." The first proposition is negative and its 
subject is described by three subordinate clauses, while 
the second proposition is affirmative and has one sub- 
ordinate clause. 

The learner may be helped by the analysis of a few sentences, 
of which the first consists of some remarkably complex lines 
from a poem of Burbidge : 

" He who metes, as we should mete, 
Could we His insight use, shall most approve, 
Not that which fills most space in earthly eyes, 
But what — though Time scarce note it as he flies — 
Fills, like this little daisy at my feet, 
Its function best of diligence in love." 

which fills most space in earthly eyes 

He shall most approve | ^ ^ filfe begt 

who metes its function of like this little 

aTw^nouldmete f^f ence in * ^ at m ? - 



could we His insight use. though Time gcarce npte it 

as he flies 



ANALYSIS OF SENTENCES. 101 

." Most sweet it is with unuplifted eyes 

To pace the ground, if path there be or none, 
While a fair region round the traveler lies 
Which he forbears again to look upon ; 
Pleased rather with some soft ideal scene, 
The work of fancy, or some happy tone 
Of meditation slipping in between, 
The beauty coming, and the beauty gone." 

Wordsworth. 

It is most sweet 

To pace the ground 



with unuplifted if path while a fair region 

eyes there i be round the I 

( or none traveler lies | 

which (region) he (the traveler) forbears to look upon 



some soft ideal scene 

ratherwith 1 tne work of fanc y 

or some happy tone of meditation 

slipping in between the beauty coming 
and the beauty gone. 

In the above sentence there is evidently one subject, " to pace 
the ground," which by means of the pronoun it, is connected with 
the predicate most sweet. The main part of the sentence, however, 
consists of three adverbials, expressing the manner and surround- 
ing circumstances, and the third adverbial is developed in a very 
complicated manner. The sentence is not compound, but is 
complex on account of four subordinate propositions. 

In the following sentence there is strictly but one principal 
proposition, "We find," but this is only a mode of introducing 
the true purport of the sentence, " the two classes of intellectual 
operations have much that is different, much that is common." 

" When the notions with which men are conversant in the 
common course of life, which give meaning to their familiar 
language and which give employment to their hourly thoughts, 
are compared with the ideas on which exact science is founded, 



102 



PROPOSITIONS. 



we find, that the two classes of intellectual operations have 

much that is different, much that is common." 

we find — that the two classes (* f) 

of intellectual j much that is different 
operations have ( much that is common 



When the notions * are compared. 



which give 
meaning 
to their 
familiar 
language 



which give with the ideas f 
employ- | 

ment to on which 

their hourly exact science is 
thoughts founded. 



with which 
men are 
conversant 
in the 
common 
course 
of life 

Here the two classes form a collective term, and have two co- 
ordinate predicates rendering the sentence so far a compound one. 
The greater part of the sentence, however, consists of a compli- 
cated subordinate sentence of the nature of an adverbial, express- 
ing the time or occasion when this is found to be the case. 
As a last example we take the sentence given below : — 
"The law of gravitation, the most universal truth at which 
human reason has yet arrived, expresses not merely the general 
fact of the mutual attraction of all matter ; not merely the vague 
statement that its influence decreases as the distance increases, 
but the exact numerical rate at which that decrease takes place ; 
so that when its amount is known at any one distance it may be 
exactly calculated for any other." 

at which human reason has yet arrived 

the most universal truth 

The law of gravitation expresses 



not merely the 
general fact 

of the mutual 

attraction of all 

matter 



not merely the 
vague statement 

that its influence 
decreases 

as the distance 
increases 



but the exact 

numerical rate 

I 

at which that 

decrease takes 

place 



so that its amount may be calculated for any other distance 
when it is known at any one distance. 



ANALYSIS OF SENTENCES. 103 

W. S. Dalgleish's Grammatical Analysis, or J. D. Morell's 

Analysis of Sentences. 
Alexander Bain's English Composition and Rhetoric, pp. 91-117, 

treats of construction of sentences. 

In this section, on "The Logical Analysis of 
Sentences," we have considered:— 

1. The Relation of Logic to this Topic. 

2. The Gh*ammatical and the Logical Predicate. 

3. The Plurality of Propositions in a Sentence, 

4. Complex Sentences. 

5. Modes of Exhibiting Construction* 



CHAPTHH Hi* 

SYLLOGISMS. 

The subject of Syllogisms will be considered 
under the following divisions : (1) The Laws of 
Thought; (2) The Mules of the Syllogism; 
(3) The Moods and Figures of the Syllo- 
gism; (4) The Reduction of Syllogisms; 

(5) Irregular and Compound Syllogisms; 

(6) Conditional Syllogisms. 



SECTION I. 
THE LAWS OF THOUGHT. 

1. The Statement of the Primary Laws of 
Thought. 

Before proceeding to examine the structure of the 
Syllogism and the rules that govern it, it is desirable 
that the learner should give a careful attention to the 
very simple laws of thought on which all reasoning 
must ultimately depend. These laws describe the very 
simplest truths, in which all people must agree, and 
which at the same time apply to all notions which we 
can conceive. It is impossible to think correctly and 
avoid evident self-contradiction unless we observe what 
are called the Three Primary Laws of Thought, which 
may be stated as follows : 



LAWS OF THOUGHT. 105 

1. The Law of Identity. Whatever is, is. 

2. The Law of Contradiction. Nothing can both be 

and not be. 

3. The Law of Excluded Middle. Everything must 

either be op not be. 

Though these laws when thus stated may seem absurdly 
obvious, and were ridiculed by Locke and others on that account, 
students are seldom able to see at first their full meaning and 
importance. All arguments may be explained when these self- 
evident laws are granted ; and it is not too much to say that the 
whole of logic will be plain to those who will constantly use 
these laws as the key. 

2. Explanation of the Laws. 

(1.) Law of Identity. — The first of the laws may be 
regarded as the best definition we can give of identity 
or sameness. Conld any one be ignorant of the mean- 
ing of the word Identity, it would be sufficient to in- 
form him that everything is identical with itself. 

(2.) Law of Contradiction. — The second law, how- 
ever, is one which requires more consideration. Its 
meaning is that nothing can have at the same time and 
at the same place contradictory and inconsistent quali- 
ties. A piece of paper may be blackened in one part, 
while it is white in other parts ; or it may be white at 
one time, and afterwards become black ; but we cannot 
conceive that it should be both white and black at the 
same place and time. A door after being open may be 
shut, but it cannot at once be shut and open. Water 
may feel warm to one hand and cold to another hand, 
but it cannot be both warm and cold to the same 
hand. No quality can both be present and absent at 



106 SYLLOGISMS. 

the same time ; and tliis seems to be the most simple 
and general truth which we can assert of all things. It 
is the very nature of existence that a thing cannot be 
otherwise than it is ; and it may be safely said that all 
fallacy and error arise from unwittingly reasoning in a 
way inconsistent with this law. All statements or in- 
ferences which imply a combination of contradictory 
qualities must be taken as impossible and false, and the 
breaking of this law is the mark of their being false. 
It can easily be shown that if Iron be a metal, and 
every metal an element, Iron must be an element or it 
can be nothing at all, since it would combine qualities 
which are inconsistent. 

(3) The Law of Excluded Middle is much less self- 
evident than either of the two preceding ones, and the 
learner will not perhaps see at the first moment that it 
is equally important and necessary with them. Its 
meaning may be best explained by saying that it is im- 
possible to mention any thing and any quality or cir- 
cumstance, without allowing that the quality op circum- 
stance either belongs to the thing or does not belong. 
The name of the law expresses the fact that there is no 
third or middle course ; the answer must be Yes or No. 
Let the thing be rock and the quality hard ; then rock 
must be either hard or not-hard. Gold must be either 
white or not white ; a line must be either straight or 
not straight ; an action must be either virtuous or not 
virtuous. Indeed, when we know nothing of the terms 
used we may nevertheless make assertions concerning 
them in accordance with this law. The learner may 
not know, and in fact chemists may not really know 
with certainty, whether vanadium is a metal or not a 



LAWS OF THOUGHT. 107 

metal, but any one knows that it must be one or the 
other. Some learners may not know what a cycloid is, 
or what an isochronous curve is ; but they must know 
that a cycloid is either an isochronous curve or it is 
not an isochronous curve. 

This law of excluded middle is not so evident but that plausible 
Objections may be suggested to it. Rock, it may be urged, is 
not always either hard or soft, for it may be half-way between, 
a little hard and a little soft at the same time. This objection 
points to a distinction which is of great logical importance, and 
when neglected often leads to fallacy. The law of excluded 
middle affirmed nothing about hard and soft, but only referred to 
hard and not-hard; if the reader chooses to substitute soft for 
not-hard he falls into a serious confusion between opposite terms 
and contradictory terms. It is quite possible that a thing may 
be neither hard nor soft, being half- way between ; but in that 
case it cannot be fairly called hard, so that the law holds true. 
Similarly water must be either warm or not-warm, but it does 
not follow that it must be warm or cold. The alternative not- 
warm evidently includes all cases in which it is cold besides 
cases where it is of a medium temperature, so that we should call 
it neither warm nor cold. We must thus carefully distinguish 
questions of degree or quantity from those of simple logical 
fact. In cases where a thing or quality may exist to a greater or 
less extent there are many alternatives. Warm water, for in- 
stance, may have any temperature from 70° perhaps up to 120°. 
Exactly the same question occurs in cases of geometrical reason- 
ing ; for Euclid in his Elements frequently argues from the self- 
evident truth that any line must be either greater than, equal to, 
or less than any other line. While there are only two alternatives 
to choose from in logic there are three in Mathematics ; thus one 
line, compared with another, may be — 

( greater greater ) j n 

In Logic. -| not greater | . . . .equal ]■ Mathematics . 

Another and even more plausible objection may be raised to 



108 SYLLOGISMS. 

the third law of thought in this way. Virtue being the thing 
proposed, and triangular the quality, the Law of Excluded 
Middle enables us at once to assert that virtue is either triangular 
or not-triangular. At first sight it might seem false and absurd 
to say that an immaterial notion such as virtue should be either 
triangular or not, because it has nothing in common with those 
material substances occupying space to which the notion of figure 
belongs. But the absurdity would arise, not from any falseness 
in the law, but from misinterpretation of the expression not- 
triangular. If in saying that a thing is "not triangular" we are 
taken to imply that it has some figure though not a triangular 
figure, then of course the expression cannot be applied to virtue 
or anything immaterial. In strict logic, however, no such im- 
plied meaning is to be allowed, and not-triangular will include 
both things which have figure other than triangular, as well as 
things which have not the properties of figure at all ; and it is 
in the latter meaning that it is applicable to an immaterial thing. 

3. The Canons of Syllogism. 

These three laws then being universally and neces- 
sarily true to whatever things they are applied, become 
the foundation of reasoning. All acts of reasoning 
proceed from certain judgments, and the act of judg- 
ment consists in comparing two things or ideas together 
and discovering whether they agree or differ, that is to 
say whether they are identical in any qualities. The 
laws of thought inform us of the very nature of this 
identity with which all thought is concerned. But in 
the operation of discourse or reasoning we need certain 
additional laws, or axioms, or self-evident truths, which 
may be thus stated : 

1. Two terms agreeing with one and the same third 
term agree with each other. 

2. Tiuo terms of which one agrees and the other does 



LAWS OF THOUGHT. 109 

not agree with one and the same third term, do not agree 
ivith each other. 

3. Two terms both disagreeing with one and the same 
third term may or may not agree ivith each other. 

These self-evident truths are commonly called the 
Canons or Fundamental Principles of Syllogism. 

They are true, whatever may be the kind of agreement in 
question. The example -we formerly used (p. 3) of the agree- 
ment of the terms " Most useful metal " and " cheapest metal " 
with the third common term " Iron," was but an instance of the 
first Canon, and the agreement consisted in complete identity. 
In the case of the "Earth," the " Planets," and "Bodies revolv- 
ing in elliptic orbits," the agreement was less complete, because 
the Earth is only one of many Planets, and the Planets only a 
small portion of all the heavenly bodies, such as Satellites, 
Comets, Meteors, and Double-Stars which revolve in such orbits. 

The second of the Canons applies to cases where there is dis- 
agreement or difference, as in the following example : 

Venus is a planet. 

Planets are not self-luminous. 

Therefore Venus is not self-luminous. 

The first of these propositions states a certain agreement to 
exist between Venus and planet, just as in the previous case of 
the Earth, but the second proposition states a disagreement be- 
tween Planet and self-luminous bodies ; hence we infer a dis- 
agreement between Venus and self-luminous body. But the 
learner will carefully observe that from two disagreements we can 
never infer anything. If the following were put forth as an 
argument it would be evidently absurd : — 

Sirius is not a planet. 
Planets are not self-luminous. 
Therefore Sirius is not self-luminous. 

Both the premises or propositions given are true, and yet the 



110 SYLLOGISMS. 

conclusion is false, for all the fixed stars are self-luminous, or 
shine by their own light. This illustrates the third Canon. 

4. The Axioms of Mathematics. 

Self-evident rules, of an exactly similar nature to 
these three Canons, are the basis of all mathematical 
reasoning, and are usually called axioms. Euclid's first 
axiom is that "Things which, are equal to the same 
thing are equal to one another;" and whether we 
apply it to the length of lines, the magnitude of angles, 
areas, solids, numbers, degrees, or anything else which 
admits of being equal or unequal, it holds true. Thus 
if the lines A and B are each equal to G it is evident 
that each is equal to the other. 

A 

B . 

C 

D. . 

E 

Euclid does not give axioms corresponding to the 
second and third Canons, but they are really used in 
Geometry. Thus if A is equal to B, but D is not 
equal to B, it follows that A is not equal to D, or 
things of which one is equal, but the other unequal to 
the same third thing, are unequal to each other. Lastly, 
A and E are two lines both unequal to D and un- 
equal to each other, whereas A and B are two lines both 
unequal to D but equal to each other; thus we plainly 
see that "two things both unequal to the same thing 
may or may not be equal to each other." 

From what precedes it will be apparent that all reasoning re- 



LAWS OF THOUGHT. Ill 

quires that there should be one agreement at least; if there 
be two agreements we may reason to a third agreement ; if there 
be one agreement and one difference we may reason to a second 
difference ; but if there be two differences only we cannot reason 
to any conclusion whatever. These self-evident principles will 
in the next Lesson serve to explain some of the rules of the 
Syllogism. 

5. Aristotle's Dicta. 

Logicians, however, have not confined themselves to 
the use of these Canons, bat have often put the same 
truth into a different form in axioms known as the 
Dicta de omni et nullo of Aristotle. This celebrated 
Latin phrase means "Statements concerning all and 
none," and the axiom, or rather pair of axioms, is 
usually given in the following words: 

Whatever is predicated of a term distributed, whether 
affirmatively or negatively, may he predicated in like 
manner of everything contained under it. 
Or more briefly : 

What pertains to the higher class pertains also to the 



This merely means, in untechnical language, that what may 
be said of all the things of any sort or kind may be said of any 
one or any part of those things ; and, secondly, what may be 
denied of all the things in a class may be denied of any one or 
any part of them. Whatever may be said of " All planets" may 
be said of Venus, the Earth, Jupiter, or any other planet ; and, 
as they may all be said to revolve in elliptic orbits, it follows 
that this may be asserted of Venus, the Earth, Jupiter, or any 
other planet. Similarly, according to the negative part of the 
Dicta, we may deny that the planets are self-luminous, and know- 
ing that Jupiter is a planet may deny that Jupiter is self-lumi- 
nous. A little reflection would show that the affirmative Dictum 
is really the first of the Canons in a less complete and general 
form, and that the negative Dictum is similarly the second 



112 SYLLOGISMS. 

Canon. These Dicta, in fact, only apply to such cases of agree- 
ment between terms as consist in one being the name of a smaller 
class, and another of the larger class containing it. Logicians 
have for the most part strangely overlooked the important cases 
in which one term agrees with another to the extent of being 
identical with it ; but this is a subject which we cannot fitly dis- 
cuss here at any length. It is treated in my little work called The 
Substitution of Similars.* 

Some logicians have held that in addition to the three laws 
which are called the Primary Laws of Thought, there is a fourth 
called "The Principle or Law of Sufficient Reason/' It was 
stated by Leibnitz in the following words : 

" Nothing happens without a reason why it should be so rather 
than otherwise. For instance, if there be a pair of scales in every 
respect exactly alike on each side and with exactly equal weights 
in each scale, it must remain motionless and in equilibrium, be- 
cause there is no reason why one side should go down more than 
the other. It is certainly a fundamental assumption in mechani- 
cal science that if a body is acted upon by two perfectly equal 
forces in different directions it will move equally between them, 
because there is no reason why it should move more to one side 
than the other. Mr. Mansel, Sir W. Hamilton and others consider, 
however, that this law has no place in logic, even if it can be 
held self-evident at all ; and the question which appears open to 
doubt need not be discussed here. 

I have so freely used the word axiom in this lesson that it is 
desirable to clear up its meaning as far as possible. Philosophers 
do not perfectly agree about its derivation or exact meaning, but 
it certainly comes from the verb dtjioa), which is rendered, to think 
worthy. It generally denotes a self evident truth of so simple a 
character that it must be assumed to be true, and, as it cannot 
be proved by any simpler proposition, must itself be taken as the 
basis of reasoning. In mathematics it is clearly used in this 
sense. 

See Hamilton's Lectures on Logic, Lectures 5 and 6. 
* Macmillan & Co., 1869. 



LAWS OF THOUGHT. 113 

In this Section, on "The Laws of Thought," we 
have considered:— 

1. Statement of the Primary Laws of Thought. 

2. The Explanation of the Laws, 

3. The Canons of the Syllogism. 

4. The Axioms of Mathematics. 

5. Aristotle's Dicta. 



SECTION II. 

THE RULES OF THE SYLLOGISM. 

1. The Definition of " Syllogism." 

Syllogism is the common name for mediate inference, 

or inference by a medium or middle term, and is to be 
distinguished from the process of immediate inference, 
or inference which is performed without the use of any 
third or middle term. 

The name Syllogism means the joining together in 
thought of two propositions, and is derived from the 
Greek words ovv, with, and Aoyoc, thought or reason. 
It is thus exactly the equivalent of the word Computa- 
tion, which means thinking together, (Latin con, to- 
gether, puto, to think), or reckoning. In a syllogism 
we so unite in thought two premises, or propositions 
put forward, that we are enabled to draw from them or 
infer, by means of the middle term they contain, a 
third proposition called the conclusion. Syllogism may 
thus be defined as the act of thought by which from 
two given propositions we proceed to a third proposi- 



114 SYLLOGISMS. 

tion, the truth of which necessarily follows from 
the truth of these given propositions. When the 
argument is fully expressed in language it is usual to 
call it concretely a syllogism. 

2. The Meaning of "Middle Term." 

We are in the habit of employing a middle term, or 
medium, whenever we are prevented from comparing 
two things together directly, but can compare each 
of them with a certain third thing. We cannot com- 
pare the sizes of two halls by placing one in the other, 
but we can measure each by a foot-rule or other suit- 
able measure, which forms a common measure, and 
enables us to ascertain with any necessary degree of 
accuracy their relative dimensions. If we have two 
quantities of cotton goods and want to compare them, it 
is not necessary to bring the whole of one portion to 
the other, but a sample is cut off, which represents 
exactly the quality of one portion, and, according as 
this sample does or does not agree with the other por- 
tion, so must the two portions of goods agree or differ. 

3. The Use of Middle Term in Syllogism. 

The use of a middle term in syllogism is closely 
parallel to what it is in the above instances, but not 
exactly the same. Suppose, as an example, that we 
wish to ascertain whether or not " Whales are vivipa- 
rous," and that we had not an opportunity of observ- 
ing the fact directly ; we could yet show It to be so it 
we knew that "whales are mammalian" animals/' and 
that "all mammalian animals are viviparous." It 
would follow that " whales are viviparous ; " and so 



LAWS OF THOUGHT. 115 

far as the inference is concerned it does not matter 
what is the meaning we attribute to the words vivip- 
arous and mammalian. In this case "mammalian 

animal " is the middle term. 

* 

4. Statement of the Rules of the Syllogism. 

The special rules of the syllogism are founded upon 
the Laws of Thought and the Canons considered in the 
previous section. They serve to inform us exactly 
under what circumstances one proposition can be in- 
ferred from two other propositions, and are eight in 
number, as follows : 

1. Every syllogism has three and only three terms. 
These terms are called the major term, the minor 

term, and the middle term. 

2. Every syllogism contains three, and only three 
propositions. 

These propositions are called the major premise, the 
minor premise, and the conclusion. 

3. The middle term must be distributed once at least, 
and must not be ambiguous. 

4. No term must be distributed in the conclusion 
which was not distributed in one of the premises. 

5. From negative premises nothing can be inferred. 

6. If one premise be negative, the conclusion must be 
negative ; and vice versa, to prove a negative conclusion 
one of the premises must be negative. 

From the above rules may be deduced two subordi- 
nate rules, which it will nevertheless be convenient to 
state at once. 

7. From two particular premises no conclusion can be 
drawn. 



116 SYLLOGISMS. 

8. If one premise he particular, the conclusion must 
he particular. 

All these rules are of such extreme importance that it will be 
desirable for the student not only to acquire a perfect comprehen- 
sion of their meaning and truth, but to commit them to memory. 
During the remainder of this section we shall consider their 
meaning and force. 

5. Explanation of the Rules. 

The following is a detailed explanation of each of the 
rules already stated : 

(1) The First Rule.— As the syllogism consists in 
comparing two terms by means of a middle term, there 
cannot of course be less than three terms, nor can there 
be more ; for if there were four terms, say A, B, C, D, 
and we compared A with B and C with D, we should 
either have no common medium at all between A and 
D, or we should require a second syllogism, so as first 
to compare A and G with B, and then A and D with 0. 

The middle term may always be known by the fact 
that it does not occur in the conclusion. The major 
term is always the predicate of the conclusion, and the 
minor term the subject. These terms are thus called 
because in the universal affirmative proposition (A) the 
predicate is necessarily a wider or greater or major 
term than the subject ; thus in "all men are mortals," 
the predicate includes all other animals as well as men, 
and is obviously a major term or wider term than men. 

(2) The Second Rule. — The syllogism necessarily 
consists of a premise called the major premise, in which 
the major and middle terms are compared together ; of 



LAWS OF THOUGHT. 117 

a minor premise which similarly compares the minor 
and middle terms; and of a conclusion, which contains 
the major and minor terms only. In a strictly correct 
syllogism the major premise always stands before the 
minor premise, but in ordinary writing and speaking 
this rule is seldom observed ; and that premise which 
contains the major term still continues to be the major 
premise, whatever may be its position. 

(3) The third rule is a very important one, because 
many fallacies arise from its neglect. By the middle 
term being distributed once at least, we mean (see p. 
79) that the whole of it must be referred to universally 
in one premise, if not both. The two propositions — 

All Frenchmen are Europeans, 

All Eussians are Europeans, 
do not distribute the middle term at all, because they 
are both affirmative propositions, which have (p. 80) 
undistributed predicates. It is apparent that French- 
men are one part of Europeans, and Eussians another 
part, as shown in Euler's method in Fig. 6, so that 

Fig. 6. 




there is no real middle term. Those propositions would 
equally allow of Eussians being or not being French- 



118 SYLLOGISMS. 

men ; for whether the two interior circles overlap or 
not they are equally within the larger circle of Euro- 
peans. Again, the two propositions 

All Frenchmen are Europeans, 
All Parisians are Europeans, 

do not enable us to infer that all Parisians are French- 
men. For though we know of course that all Parisians 

Fig. 7. 




are included among Frenchmen, the premises would 
allow of their being placed anywhere within the circle 
of Europeans. We see in this instance that the prem- 
ises and conclusion of an apparent argument may all be 
true and yet the argument may be fallacious, 

The part of the third rule which refers to an ambiguous middle 
term hardly requires explanation. It has been stated (Chap. I, 
Sect. 2.) that an ambiguous term is one which has two different 
meanings, implying different connotations, and it is really equiv- 
alent to two different terms which happen to have the same form 
of spelling, so that they are readily mistaken for each other. 
Thus if we were to argue that because " all metals are elements 
and brass is metal, therefore it is an element," we should be 
committing a fallacy by using the middle term metal in two dif- 



LAWS OF THOUGHT. 119 

ferent senses, in one of which it means the pure simple sub- 
stances known to chemists as metals, and in the other a mixture 
of metals commonly called metal in the arts, but known to 
chemists by the name alloy. In many examples which may be 
found in logical books the ambiguity of the middle term is ex- 
ceedingly obvious, but the reader should always be prepared to 
meet with cases where exceedingly subtle and difficult cases of 
ambiguity occur. Thus it might be argued that "what is right 
should be enforced by law, and that charity is right and should 
therefore be enforced by the law." Here it is evident that right 
is applied in one case to what the conscience approves, and in an- 
other case to what public opinion holds to be necessary for the 
good of society. 

(4) The fourth pule forbids us to distribute a term in 
the conclusion unless it was distributed in the premises. 
As the sole object of the syllogism is to prove the con- 
clusion by the premises, it is obvious that we must not 
make a statement concerning anything unless that 
thing was mentioned in the premises, in a way warrant- 
ing the statement. Thus if we were to argue that 
" because many nations are capable of self-government 
and that nations capable of self-government should not 
receive laws from a despotic government, therefore no 
nation should receive laws from a despotic govern- 
ment," we should be clearly exceeding the contents of 
our premises. The minor term, many nations, was 
particular in the minor premise, and must not be made 
universal in the conclusion. The premises do not 
warrant a statement concerning anything but the many 
nations capable of self-government. The above argu- 
ment would therefore be fallacious and would be tech- 
nically called an illicit process of the minor term, mean- 
ing that we have improperly treated the minor term. 



120 SYLLOGISMS. 

Such a breach of the fourth rule as is described above 
is exceedingly easy to detect, and is therefore very sel- 
dom committed. 

But an illicit process 01? improper treatment of the 
major term is more common because it is not so trans- 
parently false. If we argued indeed that "because all 
Anglo-Saxons love liberty, and Frenchmen are not 
Anglo-Saxons, therefore they do not love liberty," the 
fallacy would be pretty apparent ; but without a knowl- 
edge of logic it would not be easy to give a clear ex- 
planation of the fallacy. It is apparent that the major 
term loving liberty, is undistributed in the major prem- 
ise, so that Anglo-Saxons must be assumed to be only a 
part of those who love liberty. Hence the exclusion 
of Frenchmen from the class Anglo-Saxons does not 
necessarily exclude them from the class who love liberty 
(see Fig. 8). The conclusion of the false argument 

Fig. 8. 



Loving TAberty 

\ French } 
Anglo- \V / 

Saxons J \ / j 



being negative distributes its predicate, the major term, 
and as this is undistributed in the major premise we 
have an illicit major, as we may briefly call this fal- 
lacy. 



LAWS OF THOUGHT. 121 

The following is an obscurer example of the same fallacy : — 
"Few students are capable of excelling in many branches of 
knowledge, and such as can so excel are deserving of high com- 
mendation;" hence, "few students are deserving of high com- 
mendation." The little word " few " has here the double mean- 
ing before explained (p. 71), and means that " a few are, etc., and 
the rest are not." The conclusion is thus really a negative prop- 
osition, and distributes the major term " deserving of high com- 
mendation." But this major term is clearly undistributed in the 
major premise, which merely asserts that those who can excel in 
many branches of knowledge are deserving, but says or implies 
nothing about other students. 

(5) The fifth pule is evidently founded on the prin- 
ciple noticed in the last lesson, that inference can only 
proceed where there is agreement, and that two differ- 
ences or disagreements allow of no reasoning. Two 
terms, as the third Canon states, may both differ from 
a common term and yet may or may not differ from 
each other. Thus if we were to argue that Americans 

Fig. 9. 




are not Europeans, and Virginians are not Europeans, 
we see that both terms disagree with the middle term 
6 



VZ2 SYLLOGISMS. 

Europeans, and yet they agree between themselves. In 
other cases the two negative premises may be plainly 
true while it will be quite uncertain whether the major 
and minor terms agree or not. Thus it is true, for 
instance, that " Colonists are not Europeans and Amer- 
icans are not Europeans," but this gives us no right to 
infer that Colonists are or are not Americans. The 
two negative premises are represented in Fig. 9, by ex- 
cluding the circles of Colonists and Americans from 
that of Europeans ; but this exclusion may still be 
effected whether Colonists and Americans coincide par- 
tially, or wholly, or not at all. A breach of this rule 
of the syllogism may be conveniently called the fallacy 
of negative premises. It must not, however, be sup- 
posed that the mere occurrence of a negative particle (not 
or no) in a proposition renders it negative in the man- 
ner contemplated by this rule. Thus the argument 

" What is not compound is an element. 

Gold is not compound ; 

Therefore Gold is an element," 
contains negatives in both premises, but is nevertheless 
valid, because the negative in both cases affects the 
middle term, which is really the negative term not-com- 
pound. 

(6) The sixth rule. — The truth of the sixth rule 
depends upon that of the axiom, that if two terms 
agree with a common third term they agree with each 
other, whence, remembering that a negative proposi- 
tion asserts disagreement, it is evident that a negative 
conclusion could not be drawn from really affirmative 
premises. The corresponding negative axiom prevents 
our drawing an affirmative conclusion if either premise 



LAWS OE THOUGHT. 123 

should be really negative. Only practice, however, will 
enable the student to apply this and the preceding 
rules of the syllogism with certainty, since fallacy may 
be hidden and disguised by various forms of expression. 
Numerous examples are given at the end of the book by 
which the student may acquire facility in the analysis 
of arguments. 

The remaining rules of the syllogism, the 7th and 8th, 
are by no means of a self-evident character and are in 
fact corollaries of the first six rules, that is consequences 
which follow from them. We shall therefore have to 
show farther on that they are true consequences. We 
may call a breach of the 7th rule & fallacy of particular 
premises, and that of the 8th rule the fallacy of a uni- 
versal conclusion from a particular premise, but these 
fallacies may really be resolved into those of Illicit Pro- 
cess, or Undistributed Middle. 

For many details concerning the Aristotelian and 
Scholastic Views of the Syllogism, and of Formal 
Logic generally, see the copious critical notes to 
Mansel's edition of Aldrich's Artis Logicm Rudi- 
menta. Second Edition. Oxford. 1852. 

In this section, on "The Rules of the Syllo- 
gism," we have considered :— 

1. The Definition of {i Syllogism." 

2. The Meaning of " Middle Term." 

3. The Use of Middle Term in Syllogism. 

4z. The Statement of the Rules of the Syllogism. 
5. The Explanation of the Mules of the Syllo- 
gism. 



124 SYLLOGISMS. 



SECTION III. 

THE MOODS AND FIGURES OF THE SYLLO- 
GISM. 

1. Explanation of "Moods." 

We are now in full possession of those principles of 
reasoning, and the rules founded upon them, by which 
a true syllogism may be known from one which only 
seems to be a true one, and our task in the present sec- 
tion is to ascertain the various shapes or fashions in 
which a process of mediate inference or syllogism may 
be met with. We know that every syllogistic argument 
must contain three propositions and three distinct terms 
each occurring twice in those propositions. Each prop- 
osition of the syllogism may, so far as we yet know, be 
either affirmative or negative, universal or particular, 
so that it is not difficult to calculate the utmost possible 
number of modes in which a syllogism might conceiv- 
ably be constructed. Any one of the four propositions 
A, E, I, or O may in short be taken as a major premise, 
and joined with any one of the same form as a minor 
premise, and any one of the four again may be added 
as conclusion. We should thus obtain a series of the 
combinations or modes of joining the letters A, E, I, 0, 
a few of which are here written out : 



AAA 


AEA 


AIA 


AOA 


EAA 


EEA 


AAE 


AEE 


AIE 


AOE 


EAE 


EEE 


AAI 


AEI 


All 


AOI 


EAI 


EEI 


AAO 


AEO 


AIO 


AOO 


EAO 


&c. 



It is obvious that there will be altogether 4 x 4 x 4 or 64 



MOODS AND FIGUEES. 125 

such combinations, of which 23 only are given above. 
The student can easily write out the remainder by 
carrying on the same systematic changes of the letters. 
Thus beginning with AAA we change the right-hand 
letter successively into E, I, and 0, and then do the 
same, beginning with AEA instead ; after the middle 
letter has been carried through all its changes we begin 
to change the left-hand letter. With each change of 
this we have to repeat all the sixteen changes of the 
other letters, so that there will obviously be altogether 
64 different conceivable modes of arranging propositions 
into syllogisms. We call each of these triplets of prop- 
ositions a mood or form of the syllogism (Latin modus, 
shape). 

2. The Number of Valid Moods. 

We have to consider how many of such forms can 
really be used in valid arguments, as distinguished from 
those which break one or more of the rules of the syllo- 
gism. Thus the mood AEA would break the 6th rule, 
that if one premise be negative the conclusion must be 
so too; AIE breaks the converse part of the same rule, 
that a negative conclusion can only be proved by a 
negative premise ; while EEA, EEE, etc., break the 5th 
rule, which prohibits our reasoning at all from two 
negative premises. Examples of any of these moods 
can easily be invented, and their falsity would be very 
apparent ; thus for AEA we might take 

All Austrians are Europeans, 
No Australians are Europeans ; 
Therefore, all Australians are Austrians. 



126 SYLLOGISMS. 

Many of the 64 conceivable moods are excluded by the 
7th and 8th rules of the syllogism. Thus AIA and EIE 
break the rule, that if one premise be particular the 
conclusion must be so also, while 1 1 A, 100, 010 and 
many others, break the rule against two particular 
premises. Some combinations of propositions may break 
more than one rule ; thus 000 has both negative 
premises and particular premises, and OOA also violates 
as well the 6th rule. It is an admirable exercise in the 
use of the syllogistic rules to write out all the 64 com- 
binations and then strike out such as break any rule ; 
the task, if pursued systematically, will not be so long 
or tedious as might seem likely. It will be found that 
there are only twelve moods which escape exclusion, 
and may so far be considered good forms of reasoning, 
and these are 

AAA EAE IAI OAO 

AAI EAO (IEO) 

AEE EIO 

AEO 

All 

AOO 

Of these, however, IEO will have shortly to be rejected, 
because it will be found really to break the 4th rule, 
and involves illicit process of the major term. There 
are, then, only eleven moods of the syllogism which are 
really valid ; and we may th as account for the whole of 
the sixty-four moods. 

No. of 

Excluded by Moods. 

Negative premises, Rule 5 16 

Particular premises, " 7 12 

One negative premise, " 6 12 

One premise particular, " 8 8 



MOODS AND FIGURES. 127 

No. of 
Excluded by Moods. 

Negative conclusion, Rule 6 4 

Illicit major " 4 1 

Total excluded 53 

Valid moods 11 

Total 64 



3. Explanation of "Figures." 

We have by no means exhausted as yet all the pos- 
sible varieties of the syllogism, for we have only deter- 
mined the character, affirmative or negative, general or 
particular of the propositions, but have not decided the 
ways in which the terms may be disposed in them. 
The major term must be the predicate of the conclusion, 
but it may either be subject or predicate of the major 
premise, and similarly the minor term or subject of the 
conclusion, may be either the subject or predicate of 
the minor premise. There thus arise four different 
ways, or as they are called Figures, in which the terms 
can be disposed. These four figures of the syllogism 
are shown in the following scheme, taking 

X to denote the major term 

Y middle " 

Z minor " 





Fig. 1. 


Fig. 2. 


Fig. 3. 


Fig. 4. 


Major Premise 


Y X 


XY 


Y X 


XT 


Minor " 


Z Y 


Z Y 


Y Z 


T Z 


Conclusion 


Z X 


Z X 


Z X 


Z X 



These figures must be carefully committed to memory, 
which will best be done by noting the position of the 



128 SYLLOGISMS. 

middle term, This term stands first as subject of the 
major premise in the 1st Figure, second as predicate in 
both premises of the 2d Figure, first again as subject 
of both premises in the 3d Figure, and in an inter- 
mediate position in the 4th Figure. In the conclusion, 
of course, the major and minor terms have one fixed 
position, and when, the middle term is once correctly 
placed in any figure we easily complete the syllogism. 

The reader will hardly be pleased to hear that each of the 
eleven valid moods will have to be examined in each of the four 
figures separately, so that there are 44 cases still possible, from 
which the valid syllogisms have to be selected. Thus the mood 
AEE in the first figure would be as follows : 

All Y'a are X's, 
No Z'a are Y'a; 
Therefore No Z'a are X's. 

This would break the 4th rule and be an Illicit Major, because 
X is distributed in the conclusion, which is a negative proposi- 
tion, and not in the major premise. In the second figure it would 
be valid : 

All X's are Y'a, 

No Z'a are Y'b; 
Therefore No Z's are X's. 

In the third figure it becomes 

All Y'a are X's, 

No Y'a are Z's, 

No Z's are X's, 
and again breaks the 4th rule, as regards the major term. Lastly 
in the 4th figure it is valid, as the reader may easily satisfy him- 
self. 

4. The Valid Moods in the Different Figures. 

When all the valid moods are selected out of the 44 



MOODS AND FIGURES. 129 

possible ones, there are found to be altogether 24, which 
are as follows : 

Valid Moods of the Syllogism. 



First 


Second 


Third 


Fourth 


Figure. 


Figure. 


Figure. 


Figure. 


AAA 


EAE 


AAI 


AAI 


EAE 


AEE' 


IAI 


AEE 


All 


EIO 


All 


IAI 


EIO 


AOO 


EAO 


EAO 






OAO 


EIO 


[AAI] 


[EAO]^ 


eTo" 




[EAO] 


[AEO]. 




[AEO] 



Five of the above moods are set apart and enclosed in brackets, 
because though valid they are of little or no use. They are said 
to have a weakened conclusion, because the conclusion is par- 
ticular when a general one might have been drawn. Thus AAI, 
in the first figure is represented by the example : 
All material substances gravitate, 
All metals are material substances ; 
Therefore some metals gravitate. 
It is apparent that the conclusion only states a part of the truth, 
and that in reality all metals gravitate. It is not actually an 
erroneous conclusion, because it must be carefully remembered 
(p. 84) that the affirming of a subaltern or particular proposition 
does not deny the corresponding general proposition. It is quite 
true that some metals gravitate, and it must be true because all 
of them do so. But when we can as readily prove that all do 
gravitate it is desirable to adopt this conclusion. 

If we agree with most logicians to overlook the existence of 
the five syllogisms with weakened conclusions, there will remain 
nineteen which are at once valid and useful. In the next section 
certain ancient mnemonic lines will be furnished by which alone 
it would be possible for most persons to carry in the memory 
these 19 combinations ; but the reader will in the meantime be 
able to gather from the statement of the moods in page the 
truth of the following remarks concerning the peculiar character 
of each figure of the syllogism. 



130 SYLLOGISMS. 



5. Conclusions Proved in the Different Figures. 

(1) The first figure is the only one which proves the 
proposition A, or has A for its conclusion. It is the 
only figure, too, which can prove any one of the four 
propositions A, E, I, 0. As regards the premises, it is 
especially important to note that the major premise is 
always universal (A or E), and the minor premise affir- 
mative (A or I) : this peculiarity will be further con- 
sidered in the next lesson. 

(2) The second figure proves only negative conclu- 
sions (E or 0), and the reason is easily apparent. As 
the middle term in this figure is the predicate of both 
premises it would necessarily be undistributed in both 
premises if these were affirmatives. It follows that one 
premise must be negative and of course one only, so 
that of the major and minor terms one must be in- 
cluded or excluded wholly from the middle, and the 
other at the same time excluded or included at least 
partially. 

To illustrate this we may take X, T and Z to represent, as 
before, the major, middle and minor terms of a syllogism, and 
the four moods of this figure are then 

EAE AEE 

No X's are F's, All X's are F's, 

All Z'a are F's ; No Z'a are F's ; 

.-. No Z'a are X's. . \ No Za are X's. 

EIO AOO 

No X's are F's, All X's are F's, 

Some Z's are F's ; Some Z'a are not F's ; 

.*. Some Za are not X's. ,\ Some Z'a are not X's. 



MOODS AND FIGURES. 



131 



The nature of the moods of the second figure is clearly 
shown in the following figures : 



Fig. 11. 

(Camestres.) 




Fig. 12. 
(restino.) 




It will also be observed that in the second figure the minor 
premise may be any of the four A, E, I, 0. 

(3) The third figure only proves particulars (I or 0), 
and it always has an affirmative minor premise (A or \). 
It also contains the greatest number of moods, since in 
no case is the conclusion a weakened one. 

(4) The fourth, figure is usually considered unnatural 
and comparatively useless, because the same arguments 
can be more clearly arranged in the form of the first 
figure, which in some respects it resembles. Thus it 
proves all the propositions except A, namely, E, I, 0, 
and its first mood AAI, is in reality a weakened form of 



132 SYLLOGISMS. 

AAA in the first figure. Many logicians, including in 
recent times Sir W. Hamilton, have rejected the use of 
this figure altogether. 

It is evident that the several figures of the syllogism possess 
different characters, and logicians have thought that each figure 
was best suited for certain special purposes. A German logi- 
cian, Lambert, stated these purposes concisely, as follows : — 
" The first figure is suited to the discovery or proof of the prop- 
erties of a thing; the second to the discovery or proof of the 
distinctions between things ; the third to the discovery or proof 
of instances and exceptions ; the fourth to the discovery, or 
exclusion, of the different species of genus." 

It may be added that the moods Cesare and Camestres are often 
used in disproving a statement, because they give a universal 
negative conclusion, founded upon the exclusion of one class 
from another. Thus if any one were still to assert that light con- 
sists of material particles, it might be met by the following syllo- 
gism: 

" Material particles communicate impetus to 
whatever they strike, 
Light does not communicate impetus to 
whatever it strikes ; 
Therefore light is not material particles." 

The moods Baroko and Festino are less used, but allow of a 
particular conclusion being established. 

When we wish, however, to establish objections or exceptions 
to a general statement, which is indeed the natural way of meet- 
ing it, we employ the third figure. The statement that " all 
metals are solids " would at once be disproved by the exception 
mercury, as follows : 

Mercury is not solid, 
Mercury is a metal ; 
Therefore some metal is not solid. 
Were any one to assert that what is incomprehensible cannot 
exist, we meet it at once with the argument that Infinity is in- 
comprehensible, but that infinity certainly exists, because wc 



REDUCTION OF SYLLOGISMS. 133 

cannot otherwise explain the nature of a curve line, or of a quan- 
tity varying- continuously ; therefore something that is incompre- 
hensible exists. In this case even one exception is sufficient 
entirely to negative the proposition, which really means that 
because a thing is incomprehensible it cannot exist. But if one 
incomprehensible thing does exist, others may also ; and all 
authority is taken from the statement. 

According to the Aristotelian system the third figure must also 
be employed whenever the middle term is a singular term, be- 
cause in Aristotle's view of the subject a singular term could not 
stand as the predicate of a proposition. 

In this section, on "The Moods and Figures 
of the Syllogism," we have considered :— 

1. The Explanation of Moods. 

2. The Number of Valid Moods. 

3. The Explanation of Figures. 

4:. The Valid Moods in the Different Figures. 
5. Conclusions Proved in the Different Figures. 



SECTION IY. 

THE REDUCTION OF SYLLOGISMS. 
1. The Mnemonic Verses. 

In order to facilitate the recollection of the nineteen 
valid and useful moods of the syllogism, logicians in- 
vented, at least six centuries ago, a most curious system 
of artificial words, combined into mnemonic verses, 
which may be readily committed to memory. This 
device, however ingenious, is of a barbarous and wholly 
unscientific character ; but a knowledge of its construc- 
tion and use is still expected from the student of logic, 



134 SYLLOGISMS. 

and the verses are therefore given and explained be- 
low: 

Figure 1 i bArI ? ArA > cElArEnt, dArll, fErlOque pri- 
° ' \ oris; 

Pimm. 9 i cEsArE, cAmEstrEs, fEstlnO, bArOkO 
* gUre A ( (or f AkOrO), secundse ; 

( tertia, dArAptl, dlsAmls, dAtlsI, f El Apt- 
Figure 3. i On, bOkArdO (or dOkAmO), fErlsOn, 

( habet ; quarta, insuper addit, 

Pi^nva a j br Am An tip, cAmEnEs, dlmAaris, fEsApo 
figure 4. -j f r EsIsOn. 

The words printed in ordinary type are real Latin words, signi- 
fying that four moods whose artificial names are Barbara, Celarent, 
Darii and Ferio, belong to the first figure ; that four others be- 
long to the second; six more to the third; while the fourth 
figure moreover contains five moods. Each artificial name con- 
tains three vowels, which indicate the propositions forming a 
valid mood ; thus, GtilArwnt signifies the mood of the first figure, 
which has E for a major premise, A for the minor, and E for the 
conclusion. The artificial words altogether contain exactly the 
series of combinations of vowels shown in the scheme for the 
valid moods of the syllogism, excepting those in brackets. 

2, Explanation of the Mnemonic Verses. 

These mnemonic lines also contain indications of the 
mode in which each mood of the second, third and 
fourth figures can be proved by reduction to a corre- 
sponding mood of the first figure. Aristotle looked 
upon the first figure as a peculiarly evident and cogent 
form of argument, the Dictum de omni et nullo being 
directly applicable to it, and he therefore called it the 
Perfect Figure. The fourth figure was never recog- 
nized by him, and it is often called the Galenian figure, 



REDUCTION OF SYLLOGISMS. 135 

because the celebrated Galen is supposed to have dis- 
covered it. The second and third figures were known 
to Aristotle as the Imperfect Figures, which it was 
necessary to reduce to the first figure by certain conver- 
sions and transpositions of the premises, for which 
directions are to be found in the artificial words. These 
directions are as follows : 

s indicates that the proposition denoted by the pre- 
ceding vowel is to be converted simply. 

p indicates that the proposition is to be converted per 
accidens, or by limitation. 

m indicates that the premises of the syllogism are to 
be transposed, the major being made the minor of a 
new syllogism, and the old minor the new major. The 
m is derived from the Latin mutare, to change. 

B, C, D, F, the initial consonants of the names, in- 
dicate the moods of the first figure, which are produced 
by reduction ; thus Cesare, Camestres and Camenes 
are reducible to Celarent, Darapti, etc., to Darii, Fresi- 
son to Ferio and so on. 

k denotes that the mood must be reduced or proved 
by a distinct process called Indirect reduction, or re- 
ductio ad impossibile, which will shortly be considered. 

Examples of Reduction. 

(1) Direct Reduction. — Let us now take some syllogism, say 
in Camestres, and follow the directions for reduction. Let the 
example be 

All stars are self-luminous (1) 

All planets are not self-luminous (2) 

Therefore no planets are stars (3) 

The first s in Camestres shows that we are to convert simply 
the minor premise. The m instructs us to change the order of 



136 SYLLOGISMS. 

the premises, aud the final s to convert the conclusion simply. 
When all these changes are made we obtain 

No self-luminous bodies are planets Converse of (2) 

All stars are self-luminous (1) 

Therefore no stars are planets Converse of (3) 

This, it will be found, is a syllogism in Celarent, as might be 
known from the initial C in Camestres. 
As another example let us take Fesapo, for instance : 

No fixed stars are planets, 
All planets are round bodies : 
Therefore some round bodies are not fixed stars. 

According to the directions in the name, we are to convert 
simply the major premise, and by limitation the minor premise. 
We have then the following syllogism in Ferio : 

No planets are fixed stars, 
Some round bodies are planets ; 
Therefore some round bodies are not fixed stars. 

The reader will easily apply the same process of conversion or 
transposition to the other moods, according to the directions 
contained in their names, and the only moods it will be necessary 
to examine especially are Bramantip, Baroko and Bokardo. As 
an example of Bramantip we may take : 

All metals are material substances, 
All material substances are gravitating bodies ; 
Therefore some gravitating bodies are metals. 
The name contains the letter m, which instructs us to trans- 
pose the premises, and the letter p, which denotes conversion by 
limitation; effecting these changes we have: 

All material substances are gravitating bodies 
All metals are material substances ; 
Therefore some metals are gravitating bodies. 
This is not a syllogism in Barbara, as we might have expected, 
but is the weakened mood AAI of the first figure. It is evident 
that the premises yield the conclusion " all metals are gravitating 
bodies," and we must take the letter p to indicate in this mood 



KEDUCTION OF SYLLOGISMS. 137 

that the conclusion is weaker than it might be. In truth the 
fourth figure is so imperfect and unnatural in form, containing 
nothing but ill arranged syllogisms, which would have been 
better stated in the first figure, that Aristotle, the founder of 
logical science, never allowed the existence of the figure at all. 
It is to be regretted that so needless an addition was made to the 
somewhat complicated forms of the syllogism. 

(2) Indirect Reduction. — The moods Baroko and Bokardo give 
a good deal of trouble because they cannot be reduced directly to 
the first figure. To show the mode of treating these moods we 
will take X, Y, Z, to represent the major, middle and minor 
terms of the syllogism, and Baroko may then be stated as fol- 
lows: 

■ All X's are Y's, 

Some Z's are not Y'e ; 
Therefore Some Z's are not X's. 

Now if we convert the major premise by Contraposition (p. 89) 
we have "all not-F's are not-X's," and, making this the major 
premise of the syllogism, we have 

All not-F's are not X's, 
Some Z's are not Y's ; 
Therefore Some Z's are not X's. 

Although both the above premises appear to be negative, this 
is really a valid syllogism in Ferio, because two of the negative 
particles merely affect the middle term (see p. 184), and we have 
therefore effected the reduction of the syllogism. 

Bokardo, when similarly stated, is as follows : 
Some Y's are not X's, 
All Y's are Z's ; 
Therefore Some Z's are not X's. 

To reduce this, convert the major premise by- negation, and 
then transpose the premises. We have: 
All Y's are Z's, 
Some not-X's are Y's ; 
Therefore Gome not-X's are Z's. 

This conclusion is the converse by negation of the former con- 



138 SYLLOGISMS. 

elusion, the truth of which is thus proved by reduction to a syllo- 
gism in Darii. 

Both these moods, Baroko and Bokardo, may, however, be 
proved by a peculiar process of indirect reduction, closely anal- 
ogous to the indirect proofs often employed by Euclid in Geom- 
etry. This process consists in supposing the conclusion of the 
syllogism to be false, and its contradictory therefore true, when 
a new syllogism can easily be constructed which leads to a con- 
clusion contradictory of one of the original premises. Now it is 
absurd in logic to call in question the truth of our own premises, 
for the very purpose of argument or syllogism is to deduce a con- 
clusion which will be true when the premises are true. The syl- 
logism enables us to restate in a new form the information which 
is contained in the premises, just as a machine may deliver to us 
in a new form the material which is put into it. The machine, or 
rather the maker of the machine, is not responsible for the quality 
of the materials furnished to it, and similarly the logician is not 
responsible in the least for the truth of his premises, but only 
for their correct treatment. He must treat them, if he treat them 
at all, as true ; and therefore a conclusion which requires the 
falsity of one of our premises is altogether absurd. 

To apply this method we may take Baroko, as before : 

All X's are Y's (1) 

Some Z's are not Y's (2) 

Therefore Some Z's are not X's (3) 

If this conclusion be not true then its contradictory, "all Z's 
are X's," must of necessity be regarded as true (page 84). 
Making this the minor premise of a new syllogism with the 
original major premise we have : 

All X's are Y's (1) 

All Z's are X's contradictory of (3) 

Hence All Z's are Y's. 

Now this conclusion in A, is the contradictory of our old minor 
premise in 0, and we must either admit one of our own. premises 
to be false or allow that our original conclusion is true. The 
latter is of course the alternative we choose. 



DEDUCTION Otf SYLLOGISMS. 139 

We treat Bokardo in a very similar manner : 

Some Y's are not X's (1) 

All Y's area's (2) 

Therefore Some Z's are not X's (3) 

If this conclusion be not true, then "all Z's are .X's" must be 
true. Now we can make the syllogism : 

All Z's are X's Contradictory of (3) 

All F's are Z's (2) 

Hence All F's are X's. 

This conclusion is the contradictory of (1), the original major 
premise, and as this cannot be allowed, we must either suppose 
(2) the original minor premise to be false, which is equally im- 
possible, or allow that our original conclusion is true. 

It will be observed that in both these cases of Indirect Reduc- 
tion or Proof we use a syllogism in Barbara, which fact is indi- 
cated by the initial letters of Baroko and Bokardo. The same 
process of Indirect proof may be applied to any of the other 
moods, but it is not usual to do so, as the simpler process of 
direct or as it is often called ostensive reduction is sufficient. 

3. Conclusions from Particular Premises. 

It will be remembered that when in Section 2 we 
considered the rules of the syllogism, there were two 
supplementary rules, the 7th and 8th, concerning par- 
ticular premises, which were by no means of a self- 
evident character, and which require to be proved by 
the six more fundamental rules. We have now suffi- 
ciently advanced to consider this proof with advantage. 
The 7th rule forbids us to draw any conclusion from 
two particular premises ; now such premises must be 
either II, 10, 01, or 00. Of these II contain no dis- 
tributed term at all, so that the 3d rule, which requires 
the middle term to be distributed, must be broken. 
The premises 00 evidently break the 5th rule, against 



140 SYLLOGISMS. 

negative premises. The conclusion cf the j>air 10 must 
be negative by the 6th rule, because one premise is 
negative; the major term therefore will be distributed, 
but as the major premise is a particular affirmative it 
cannot be distributed without committing the fallacy 
of illicit process of the major, against rule 4. Lastly, 
the premises 01 contain only one distributed term, the 
predicate of the major premise. But as the conclusion 
must be negative by rule 6th, the major term must be 
distributed : we ought to have then in the premises two 
distributed terms, one for the middle term, the other 
for the major term ; but as the premises contain only a 
single distributed term, we must commit the fallacy 
either of undistributed middle or of illicit process of 
the major term, if we attempt to draw any conclusion 
at all. We thus see that in no possible case can a pair 
of particular premises give a valid conclusion. 

The 8th rule of the syllogism instructs us that if 
one premise of a syllogism be particular the conclusion 
must also be particular. It can only be shown to be 
true by going over all the possible cases and observing 
that the six principal rules of the syllogism always re- 
quire the conclusion to be particular. Suppose, for in- 
stance, the premises are A and I ; then they contain 
only one distributed term, the subject of A, and this is 
required for the middle term by rule 3. Hence the 
minor term cannot be distributed without breaking 
rule 4, so that the conclusion must be the proposition I. 
The premises AO would contain two distributed terms, 
the subject of A and the predicate of ; but if we were 
to draw from them the conclusion E, the major and 
minor terms would require to be distributed, so that 



IRREGULAE AND COMPOUND SYLLOGISMS. 141 

the middle term would remain undistributed against 
rule 3. The learner can easily prove the other cases 
such as El by calculating the number of distributed 
terms in a similar manner : it will always be found that 
there are insufficient terms distributed in the premises 
to allow of a universal conclusion. 

In this section, on "The Reduction of Syllo- 
gisms," we have considered : — 

1. The Mnemonic Verses. 

2. The Explanation of the Mnenomic Versee. 

3. Conclusions from Particular Premises. 



SECTION Y- 

IRREGULAR AND COMPOUND SYLLOGISMS. 

1. The Irregular Mode of Expressing Inferences. 

It may seem surprising that arguments which are 
met with in books or conversation are seldom thrown 
into the form of regular syllogisms. Even if a com- 
plete syllogism be sometimes met with, it is generally 
employed in mere affectation of logical precision. In 
former centuries it was, indeed, the practice for all 
students at the universities to take part in public dis- 
putations, during which elaborate syllogistic arguments 
were put forward by one side and confuted by precise 
syllogisms on the other side. This practice has not 
been very long discontinued at the University of Ox- 
ford, and is said to be still maintained in some conti- 



142 SYLLOGISMS. 

nental universities ; but except in such school disputa- 
tions it must be allowed that perfectly formal syllo- 
gisms are seldom employed. 

In truth, however, it is not syllogistic arguments which 
are wanting; wherever any one of the conjunctions, there- 
fore, because, for, since, inasmuch as, consequently occurs, it is 
certain that an inference is being drawn, and this will very prob- 
ably be done by a true syllogism. It is merely the complete 
statement of the premises and conclusion, which is usually 
neglected because the reader is generally aware of one or other 
of the premises, or he can readily divine what is assumed ; and 
it is tedious and even offensive to state at full length what the 
reader is already aware of. Thus, if I say "atmospheric air 
must have weight because it is a material substance," I certainly 
employ a syllogism ; but I think it quite needless to state the 
premise, of which I clearly assume the truth, that " whatever 
is a material substance has weight." The conclusion of the 
syllogism is the first proposition, viz., "atmospheric air has 
weight." The middle term is "material substance," which does 
not occur in the conclusion 3 the minor is " atmospheric air," and 
the major, "having weight." The complete syllogism is evi- 
dently : 

All material substances have weight, 
Atmospheric air is a material substance ; 
Therefore atmospheric air has weight. 

This is in the very common and useful mood Barbara. 

2. Explanation of " Enthymeme." 

A syllogism when incompletely stated is usually called 
an enthymeme, and this name is often supposed to be 
derived from two Greek words (ev, in, and dvpoc,, mind), 
so as to signify that some knowledge is held by the 
mind and is supplied in the form of a tacit, that is a 
silent or understood premise. Most commonly this 



IEKEGULAR AKD COMPOUND SYLLOGISMS. .143 

will be the major premise, and then the enthymeme 
may be said to be of the First Order. Less commonly 
the minor premise is unexpressed, and the enthymeme 
is of the Second Order. Of this nature is the follow- 
ing argument: "Comets must be subject to the law of 
gravitation ; for this is true of all bodies which move in 
elliptic orbits." It is so clearly implied that comets 
move in elliptic orbits, that it would be tedious to state 
this as the minor premise in a complete syllogism of 
the mood Barbara, thus : 

All bodies moving in elliptic orbits are subject to the 
law of gravitation ; 

Comets move in elliptic orbits ; 

Therefore comets are subject to the law of gravita- 
tion. 

It may happen occasionally that the conclusion of a 
syllogism is left unexpressed, and the enthymeme may 
then be said to belong to the Third Order. This occurs 
in the case of epigrams or other witty sayings, of which 
the very wit often consists in making an unexpressed 
truth apparent. Sir W. Hamilton gives as an instance 
pf this kind of enthymeme the celebrated epigram 
written by Porson the English scholar upon a contem- 
porary German scholar : 

" The Germans in Greek 
Are sadly to seek ; 
Not five in five score, 
But ninety-five more ; 
All, save only Hermann, 
And Hermann's a German." 

It is evident that while pretending to make an excep- 



144 SYLLOGISMS. 

tion of Hermann, the writer ingeniously insinuates 
that since he is a German he has not a correct knowl- 
edge of Greek. The wonderful speech of Antony_over 
the body of Caesar, in Shakspeare's greatest historical 
play, contains a series of syllogistic arguments of which 
the conclusions are suggested only. 

Even a single proposition may have a syllogistic 
force if it clearly suggest to the mind a second premise 
which thus enables a conclusion to be drawn. The ex- 
pression of Home Tooke, " Men who have no rights 
cannot justly complain of any wrongs," seems to be a 
case in point ; for there are few people who have not 
felt wronged at some time or other, and they would 
therefore be likely to argue, whether upon true or false 
premises, as follows : 

Men who have no rights cannot justly complain of 

any wrongs ; 
We can justly complain ; 
Therefore we are not men who have no rights. 

In other words, we have rights. 

3. Prosyllogisms and Episyllogisms. 

Syllogisms may be variously joined and combined 
together, and it is convenient to have special names for 
the several parts of a complex argument. Thus a syl- 
logism which proves or furnishes a reason for one of 
the premises of another syllogism is called a Prosyllo- 
gism ; and a syllogism which contains as a premise the 
conclusion of another syllogism is called an Episyllo- 
cjism. 



IEEEGULAR AND COMPOUND SYLLOGISMS. 145 

Take the example : 

All B'b are A% 
All C's area's; 
Therefore all C's are A's. 
But all B'b are C's ; 
Therefore All B'b are A'b. 

This evidently contains two syllogisms in the mood 
Barbara, the first of which is a Prosyllogism with 
respect to the second, while the second is an Episyllo- 
gism with respect to the first. 

The peculiar name Epicheirema is given to a syllo- 
gism when either premise is proved or supported by a 
reason implying the existence of an imperfectly ex- 
pressed prosyllogism; thus the form, 

All -B's are A% for they are P's, 
And all C's are B's, for they are Q's; 
Therefore all C's are A% 
is a double Epicheirema, containing reasons for both 
premises. The- reader will readily decompose it into 
three complete syllogisms of the mood Barbara. 

4. Sorites. 

A more interesting form of reasoning is found in the 
chain of syllogisms commonly called the Sorites, from 
the Greek word oupog, meaning heap. It is usually 
stated in this way : 

All A'b are B% 
All B's are C's, 
All C's are D% 
All B'b are E'b ; 
Therefore all A'b are B's. 

7 . .-, . 



146 SYLLOGISMS. 

The chain can be carried on to any length provided it 
is perfectly consecutive, so that each term except the 
first and last occurs twice, once as subject and once as 
predicate. It hardly needs to be pointed out that the 
sorites really contains a series of syllogisms imperfectly 
expressed; thus 

First Syllogism. Second Syllogism. Last Syllogism. 

B's are C% C's are D's ; D's are ^'s. 

A's are B's ; A's are C's; A's are D's; 

.*. A's are C's. /. A's are D's. .: A's are U's. 

Each syllogism furnishes a premise to the succeeding 
one, of which it is therefore the prosyllogism, and any 
syllogism may equally he considered the episyllogism of 
that which precedes. 

In the above sorites all the premises were universal 
and affirmative, but a sorites may contain one particu- 
lar premise provided it be the first, and one negative 
premise provided it be the last. The learner may 
easily assure himself by trial, that if any premise except 
the first were particular the fallacy of undistributed 
middle would be committed, because one of the middle 
terms would be the predicate of one affirmative premise 
and the subject of another particular premise. If any 
premise but the last were negative there would be a 
fallacy of illicit process of the major term. 

It is not to be supposed that the forms of the syllogism 
hitherto described are all the kinds of reasoning actually 
employed in science or common life. In addition to the hypo- 
thetical and disjunctive syllogisms and some other forms to be 
described in succeeding sections, there are really many modes of 
reasoning of which logicians have not taken much notice as 
yet. This was clearly pointed out more than two hundred years 



IRREGULAR AND COMPOUND SYLLOGISMS. 147 

ago by the writers of the Port Royal Logic, a work first printed 
in the year 1662, but which has since been reprinted very often, 
and translated into a great many languages. The book is named 
from a place near Paris where a small religious community lived, 
of which the authors of the book, namely Arnauld and Nicole, 
and a contributor to it the great philosopher and mathematician 
Pascal, were the most celebrated members. The Port Royal 
Logic was to a considerable extent the basis of the well-known 
Watts' Logic, but the reader can now be referred to an admirable 
translation of the original work made by Professor Spencer 
Baynes of St. Andrew's. 

Many improvements of Logic may be found in this work, such 
as the doctrine of Extension and Intension, already explained. 
In the Ninth Chapter of the Third Part, moreover, it is wisely 
pointed out that "little pains are taken in applying the rules of 
the syllogism to reasonings of which the propositions are com- 
plex, though this is often very difficult, and there are many 
arguments of this nature which appear bad, but which are never- 
theless very good ; and besides, the use of such reasonings is 
much more frequent than that of syllogisms which are quite 
simple." Some examples are given of the complex syllogisms 
here referred to ; thus : 

The sun is a thing insensible, 
The Persians worship the sun ; 

Therefore the Persians worship a thing insensible. 

This is an argument which cannot be proved by the rules of 
the syllogism, and yet it is not only evidently true, but is an ex- 
ceedingly common kind of argument. Another example is as 
follows : 

The Divine Law commands us to honor kings; 

Louis XIV is a king ; 

Therefore the Divine Law commands us to honor Louis XIV. 

The reader will also find that arguments which are really quite 
valid and syllogistic are expressed in language so that they 
appear to have four distinct terms, and thus to break one of the 
rules of the syllogism. Thus, if I say "Diamonds are combus- 
tible, for they are composed of carbon and carbon is combustible," 



148 SYLLOGISMS. 

there are four terms employed, namely, diamonds, combustible, 
composed of carbon, and carbon. But it is easy to alter the con- 
struction of the propositions so as to get a simple syllogism with- 
out really altering the sense, and we then have : 

What is composed of carbon is combustible ; 

Diamonds are composed of carbon ; 

Therefore diamonds are combustible. 

Examples are given at the end of the book of concise argu- 
ments, taken from Bacon's Essays and other writings, which the 
student can reduce to the syllogistic form by easy alterations ; 
but it should be clearly understood that these changes are of an 
extra-logical character, and belong more properly to the science 
of language. 

5. Syllogisms in Extension and in Intension, 

It may here be explained that the syllogism and the 
sorites can be expressed either in the order of exten- 
sion or that of intension. In regard to the number of 
individual things the noble metals are part of the 
metals, and the metals are part of the elements ; but in 
regard to intension, that is to say the qualities implied 
in the names, element is part of metal, and metal is 
part of noble metal. So again in extension the genus 
of plants Anemone is part of the order Eanunculacese, 
and this is part of the great class Exogens; but in in- 
tension the character of Exogen is part of the character 
of Eanunculaceae, and this is part of the character of 
Anemone. Syllogistic reasoning is equally valid and 
evident in either case, and we might represent the two 
modes in ordinary language as follows : 

Extensive Syllogism. 
All Ranunculacese are Exogens ; 
The Anemone is one of the Ranunculaceae ; 
Therefore the Anemone is an Exogen. 



CONDITIONAL SYLLOGISMS. 149 

Intensive Syllogism. 

All the qualities of Ranunculacese are qualities of Anemone ; 
All the qualities of Exogen are qualities of Ranunculaceae ; 
Therefore all the qualities of Exogen are qualities of Anemone. 

Any sorites can be similarly represented either in extension or 
intension. 

Concerning the Aristotelian doctrine of the En thyme me, see 
Mansel's Aldrich, App., Note F, and Hamilton's Lectures on 
Logic, Lecture XX. Port Boyal Logic, translated by T. 
Spencer Baynes, 5th ed. Edinburgh, 1861. 

In this section, on "Irregular and Compound 
Syllogisms," we have considered: 

1. The Irregular Mode of Expressing Infer - 
ences. 

2. The Explanation of Enthymeme, 

3. Prosyllogisms and Episyllogisms. 

4. Sorites. 

5. Syllogisms in Extension and Intension, 



SECTION YI. 

CONDITIONAL SYLLOGISMS. . 

1. Classification of Propositions. 

It will be remembered that when treating of propo- 
sitions we divided them into two distinct kinds, Cate- 
gorical Propositions, and Conditional Propositions. 
The former kind alone has hitherto been considered, 
and we must now proceed to describe Conditional 
propositions and the arguments which may be com- 
posed of them. 



150 SYLLOGISMS. 

Logicians have commonly described Conditional prop- 
ositions as composed of two or more Categorical propo- 
sitions united by a conjunction. This union may 
happen in two ways, giving rise to two very different 
species of conditionals, which we shall call Hypothetical 
Propositions and Disjunctive Propositions. The way 
in which the several kinds of propositions are related 
will be seen in the following diagram : 

( Categorical, 
Propositions are J .(Hypothetical. 

( Conditional j D j^ nctive . 

2. Antecedent and Consequent. 

A conditional proposition may be further described 
as one which makes a statement under a certain con- 
dition or qualification restricting its application. In 
the hypothetical form this condition is introduced by 
the conjunction if, or some other word equivalent to 
it. Thus— 

"If iron is impure, it is brittle" 

is a hypothetical proposition consisting of two distinct 
categorical propositions, the first of which, "Iron is 
impure," is called the Antecedent ; the second, " It is 
brittle," the Consequent. In this case " impurity " is 
the condition or qualification which limits the applica- 
tion of the predicate brittle to iron. 

It was asserted by Home Tooke in his celebrated work, The 
Diversions of Purley, that all conjunctions are the remains or 
corrupted forms of verbs. This is certainly true in the case of 
the hypothetical conj unction ; for the word if in old English is 
written gif or gyf, and is undoubtedly derived from the verb to 



CONDITIONAL SYLLOGISMS. 151 

give. We may actually substitute at present any verb of similar 
meaning, as for instance — grant, allow, suppose. Thus, we may 

say— 

" Grant that iron is impure, and it is brittle." 
" Supposing that iron is impure, it is brittle." 

3. Kinds of Hypothetical Syllogisms. 

The hypothetical proposition might be employed in 
arguments of various form, but only two of these are 
of sufficient importance to receive special names. The 
hypothetical syllogism consists of two premises, called 
the major and minor, as in the case of the ordinary 
syllogism. The major premise is hypothetical in form ; 
the minor premise is categorical, and according as it is 
affirmative or negative the argument is said to be a 
Constructive or a Destructive hypothetical syllogism. 
Thus the form, 

If A isB, CisD; 

But A is B ; 

Therefore G is D, 
is a constructive hypothetical syllogism. 

It must be carefully observed that the minor premise 
affirms the antecedent of the major premise, whence 
the argument is said to be of the modus ponens, or 
mood which posits or affirms. It is probably one of 
the most familiar and common kinds of argument. 
The form, 

If A isB, CisD; 

But Cis not D; 

Therefore A is not B, 

represents the corresponding Destructive hypothetical 
syllogism, also called the modus tollens, or the mood 
which removes the consequent. It must be carefully 



152 SYLLOGISMS. 

observed again that it is the consequent, not the ante- 
cedent, which is denied. 

4. The Rule for Hypothetical Syllogisms. 

The only rule which is requisite for testing the 
validity of such syllogisms embodies what we have 
observed above, viz., that either the antecedent must 
be affirmed, op the consequent denied. If either part 
of this rule be broken, a serious fallacy will be com- 
mitted. Thus the apparent argument, 

If A is B, CisD; 
But CisD; 
Therefore A is B, 

is really a fallacy which we may call the fallacy of affirm- 
ing the consequent, and its fallacious nature is readily 
understood by reflecting that " A being B" is not stated 
to be the only condition on which C is D. It may 
happen that when E is F, or G is H, or under a hun- 
dred other circumstances, is D, so that the mere fact 
of being D is no sufficient proof that A is B. Thus, 
if a man's character be avaricious he will refuse to give 
money for useful purposes ; but it does not follow that 
every person who refuses to give money for such pur- 
poses is avaricious. There may be many proper reasons 
or motives leading him to refuse ; he may have no 
money, or he may consider the purpose not a useful 
one, or he may have more useful purposes in view. 
A corresponding fallacy arises from denying the ante- 
t, as in the form — 

If A is B, Ci&D; 

But A is not B ; 
Therefore O is not D. 



CONDITIONAL SYLLOGISMS. 153 

The error may be explained in the same way; for as 
"A being B " is not stated to be the only condition of 
C being D, we may deny this one condition to be true, 
but it is possible that the consequent may happen to be 
true for other reasons, of which we know nothing. 
Thus if a man is not avaricious we cannot conclude 
that he will be sure to give money whenever asked. 
Or take the following example : 

" If the study of Logic furnished the mind with a 
multitude of useful facts like the study of other sciences, 
it would deserve cultivation ; but it does not furnish 
the mind with a multitude of useful facts ; therefore it 
does not deserve. cultivation." 

This is evidently a fallacious argument, because the 
acquiring of a multitude of useful facts is not the only 
ground on which the study of a science can be recom- 
mended. To correct and exercise the powers of judg- 
ment and reasoning is the object for which Logic 
deserves to be cultivated, and the existence of such 
other purpose is ignored in the above fallacious argu- 
ment, which evidently involves the denial of the ante- 
cedent. 



5. The Reduction of Hypothetical to Categorical 
Syllogisms. 

Although it is usual in logical works to describe the 
hypothetical proposition and syllogism as if they were 
different in nature from the categorical proposition and 
syllogism, yet it has long been known that the hypo- 
theticals can be reduced to the categorical form, and 
brought under the ordinary rules of the syllogism. As 



154 SYLLOGISMS. 

a general rule the hypothetical proposition can be 
readily converted into a universal affirmative proposi- 
tion (A) of exactly the same meaning. Thus our 
instance, "If iron is impure, it is brittle/' becomes 
simply, "Impure Iron is brittle." In making this 
alteration in a hypothetical syllogism it will be found 
necessary to supply a new minor term ; thus in the 
case, 

If iron is impure it is brittle ; 

But it is impure ; 

Therefore it is brittle, 

we have to substitute for the indefinite pronoun it, the 
iron in question, and we obtain a correct categorical 
syllogism in the mood Barbara : 

Impure iron is brittle ; 

The iron in question is impure iron ; 

Therefore the iron in question is brittle. 

Sometimes the reduction requires a more extensive change 
of language. For instance, 

If the barometer is falling, bad weather is coining ; 
But the barometer is falling ; 
Therefore bad weather is coming, 
may be represented in the following form : 

The circumstances of the barometer falling are the circumstances 

of bad weather coming ; 
But thesp are the circumstances of the barometer falling ; 
Therefore these are the circumstances of bad weather coming. 

As an instance of the Destructive Hypothetical syllogism we 
may take : 

If Aristotle is right, slavery is a proper form of society ; 
But slavery is not a proper form of society ; 
Therefore Aristotle is not right. 



OOKDITIOKAL SYLLOGISMS. 155 

This becomes as a categorical • 

The case of Aristotle being right is the case of slavery being a 

proper form of society; 
But this is not the case ; 
Therefore this is not the case of Aristotle being right. 

If not reducible by any other form of expression, hypothetical 
can always be reduced by the use of the words case of. 

6. Fallacies in Hypothetical Syllogisms. 

It will now be easily made apparent that the fallacy 
of affirming the consequent is really a breach of the 
third rule of the syllogism, leading to an undistributed 
middle term. Our example may be as before : 

If a man is avaricious he will refuse money ; 
But he does refuse money ; 
Therefore he is avaricious. 

This becomes as a categorical syllogism, 
All avaricious men refuse money ; 
But this man refuses money ; 
Therefore this man is avaricious. 

This is the mood AAA in the second figure ; and the 
middle term, refusing money, is undistributed in both 
premises, so that the argument is entirely fallacious. 

Again, the fallacy of denying the antecedent is equiv- 
alent to the illicit process of the major. Our former 
example (p. 153) may thus be represented: 

" A science which furnishes the mind with a multi- 
tude of useful facts deserves cultivation ; but Logic is 
not such a science; therefore Logic does not deserve 
cultivation." 



156 Syllogisms. 

ThLs apparent syllogism is of the mood AEE in the 
first figure, which breaks the fourth rule of the syllo- 
gism, because the major term, deserving cultivation, is 
distributed in the negative conclusion, but not in the 
affirmative major premise. 

7. Disjunctive Syllogisms. 

We now pass to the consideration of the disjunctive 
proposition, which instead of a single predicate has 
several alternatives united by the disjunctive conjunc- 
tion or, any one of which may be affirmed of the subject. 
"A member of the House of Commons is either a repre- 
sentative of a county, or of a borough, or of a Univer- 
sity," is an instance of such a proposition, containing 
three alternatives ; but there may be any number of 
alternatives from two upwards. 

The disjunctive syllogism consists of a disjunctive 
major premise with a categorical proposition, either 
affirmative or negative, forming the minor premise. 
Thus arise two moods : 

(1) The affirmative mood is called by the Latin words 
modus ponendo tollens (the mood which by affirming 
denies), and may be thus stated : 

A is either B or C, 
But A is B ; 
Therefore A is not C. 

This form of argument proceeds on the supposition 
that if one alternative of a disjunctive proposition be 
held true, the others cannot also be true. Thus "the 
time of year must be either spring, summer, autumn or 
winter," and if it be spring it cannot be summer, 



CONDITIONAL SYLLOGISMS. 157 

autumn or winter ; and so on. But it has been ob- 
jected by Whately, Mansel, Mill, as well as many 
earlier logicians, that this does not always hold true. 
Thus if we say that "a good book is valued either for 
the usefulness of its contents or the excellence of its 
style, " it does not by any means follow because the con- 
tents of a book are useful that its style is not excel- 
lent. We generally choose alternatives which are in- 
consistent with each other ; but this is not logically 
necessary. 

(2) The other form of disjunctive syllogism, called 
the modus tollendo ponens (the mood which by deny- 
ing affirms), is always of necessity cogent, and is as 
follows: 

A is either B or C, 

But A is not B; 

Therefore A is C. 

Thus if we suppose a book to be valued only for the 
usefulness of its contents or the excellence of its style, 
it follows that if a book be valued, but not for the 
former reason, it must be for the latter ; and vice versa. 
If the time of year be not spring, it must be summer, 
autumn or winter ; if it be not autumn nor winter, it 
must be either spring or summer ; and so on. In short 
if any alternatives be denied, the rest remain to be 
affirmed as before. It will be noticed that the disjunc- 
tive syllogism is governed by totally different rules 
from the ordinary categorical syllogism, since a nega- 
tive premise gives an affirmative conclusion in the 
former, and a negative conclusion in the latter. 



158 SYLLOGISMS. 

8. The Dilemma. 

There yet remains a form of argument called the 
Dilemma, because it consists in assuming two alterna- 
tives, usually called the horns of the dilemma, and yet 
proves something in either case (Greek, di- two ; XfjpLfia, 
assumption). Mr. Mansel defines this argument as " a 
syllogism, having a conditional major premise with more 
than one antecedent, and a disjunctive minor." There 
are at least three forms in which it may be stated. 

(1) The first form is called the Simple Constructive 
Dilemma : 

If A isB, CisD; and if .# is i^, CisD; 
But either A is B, or E is F; 
Therefore C is D. 

Thus "if a science furnishes useful facts, it is worthy 
of being cultivated ; and if the study of it exercises the 
reasoning powers, it is worthy of being cultivated ; but 
either a science furnishes useful facts, or its study exer- 
cises the reasoning powers; therefore it is worthy of 
being cultivated." 

(2) The second form of dilemma is the Complex Con- 
structive Dilemma, which is as follows: 

If A is B, CisD; and if ^ is F, G is H; 
But either A is B, or E is F; 
Therefore either (7 is D, or G is H. 

It is called complex because the conclusion is in the 
disjunctive form. As an instance we may take the 
argument, " If a statesman who sees his former opinions 
to be wrong does not alter his course, he is guilty of 
deceit; and if he does alter his course, he is open to a 



! J j i 

COjSDmOSTAL SYLLOGISMS. 159 

charge of inconsistency ; but either he does not alter 
his course, or he does ; therefore he is either guilty of 
deceit, or he is open to a charge of inconsistency." In 
this case, as in the greater number of dilemmas, the 
terms A, B, C, D, etc., are not all different. 

(3) The Destructive Dilemma is always complex, be- 
cause it could otherwise be resolved into two uncon- 
nected destructive hypothetical syllogisms. It is in the 
following form : 

If A is B, CisD; and if ^is F, is H ; 
But either C is not D, or 67 is no + . H ; 
Therefore either A is not B, or E is not F. 

For instance, " If this man were wise, he would not 
speak irreverently of Scripture in jest ; and if he were 
good, he would not do so in earnest ; but he does it 
either in jest or earnest ; therefore he is either not wise, 
or not good." * 

Dilemmatic arguments are, however, more often fallacious 
than not, because it is seldom possible to find instances where 
two alternatives exhaust all the possible cases, unless indeed one 
of them be the simple negative of the other in accordance with 
the law of excluded middle. Thus if we were to argue that " if 
a pupil is fond of learning he needs no stimulus, and that if he 
dislikes learning no stimulus will be of any avail, but as he is 
either fond of learning or dislikes it, a stimulus is either needless 
or of no avail," we evidently assume improperly the disjunctive 
minor premise. Fondness and dislike are not the only two pos- 
sible alternatives, for there may be some who are neither fond of 
learning nor dislike it, and to these a stimulus in the shape of 
rewards may be desirable. Almost anything can be proved if we 



Whately. 



160 SYLLOGISMS. 

are allowed thus to pick out two of the possible alternatives 
which are in our favor, and argue from these alone. 

A dilemma can often be retorted by producing as cogent a 
dilemma to the contrary effect. Thus an Athenian mother, ac- 
cording to Aristotle, addressed her son in the following words : 
"Do not enter into public business ; for if you say what is just, 
men will hate you ; and if you say what is unjust the gods will 
hate you." To which Aristotle suggests the following retort : "I 
ought to enter into public affairs ; for if I say what is just, the 
gods will love me ; and if I say what is unjust, men will love 
me." 

Mansel's Aldrich, App. Note I, on the Hypothetical Syllogism. 

In this section, on "Conditional Syllogisms," 
we have considered:— 

1. The Classification of Propositions. 

2. Antecedent and Consequent. 

3. The Kinds of Hypothetical Syllogisms. 

4. The Rale for Hypothetical Syllogisms, 

5. The Reduction of Hypothetical Syllogisms to 

Categorical Syllogisms. 

6. Fallacies in Hypothetical Syllogisms. 

7. Disjunctive Syllogisms. 

8. The Dilemma. 



CHAPTER IV. 

FALLACIES. 

In order to acquire a satisfactory knowledge of the 
rules of correct thinking, it is essential that we should 
become acquainted with the most common kinds of 
fallacy; that is to say, the modes in which, by neglect- 
ing the rules of logic, we often fall into erroneous 
reasoning. In previous lessons we have considered, as 
it were, how to find the right road ; it is our task here 
to ascertain the turnings at which we are most liable to 
take the wrong road. 

In describing the fallacies, I shall follow the order 
and adopt the mode of classification which has been 
usual for the last 2000 years and more, since in fact 
the great teacher Aristotle first explained the fallacies. 
According to this mode of arrangement fallacies are 
divided into two principal groups, containing the logi- 
cal and the material fallacies. 

1. The logical fallacies are those which occur in the 
mere form of the statement ; or, as it is said in the old 
Latin expressions, in dictione, or in voce. It is supposed 
accordingly that fallacies of this kind can be discovered 
without a knowledge of the subject-matter with which 
the argument is concerned. 

2. The material fallacies, on the contrary, arise out- 
side of the mere verbal statement, or, as it is said, extra 
dictionem; they are concerned consequently, with the 



162 FALLACIES. 

subject of the argument, or in re (in the matter), and 
cannot be detected and set right but by those acquainted 
with the subject. 

These two classes of fallacies will now be considered 
in the following sections : (1) Logical Fallacies ; 
(2) Material Fallacies. 



SECTION !♦ 
LOGICAL FALLACIES. 

1. Classification of Logical Fallacies. 

The logical fallacies may be divided into the purely 
logical and semi-logical, and we may include in the 
former class the distinct breaches of the syllogistic 
rules which have already been described. 

(1) We may enumerate as Purely Logical Fallacies : 

1. Fallacy of four terms (Quaternio Terminorum) — 
Breach of Rule 1 ; 

2. Fallacy of undistributed middle — Breach of Rule 3 ; 

3. Fallacy of illicit process, of the major or minor 
term — Breach of Rule 4 ; 

4. Fallacy of negative premises — Breach of Rule 5 ; 
as well as breaches of the 6th rule, to which no distinct 
name has been given. 'Breaches of the 7th and 8th 
rules may be resolved into the preceding (p. 140), but 
they may also be described as in p. 123. 

(2) The other part of the class of logical fallacies con- 
tains Semi-logical fallacies, which are six in number, 
as follows : 



LOGICAL FALLACIES. 163 

1. Fallacy of Equivocation. 

2. Fallacy of Amphibology. 

3. Fallacy of Composition. 

4. Fallacy of Division. 

5. Fallacy of Accent. 

6. Fallacy of Figure of Speech. 

These I shall describe and illustrate in succession. 



2. The Fallacy of Equivocation. 

Equivocation consists in the same term being used in 
two distinct senses ; any of the three terms of the syllo- 
gism may be subject to this fallacy, but it is usually the 
middle term which is used in one sense in one premise 
and in another sense in the other. In this case it is 
often called the fallacy of ambiguous middle, and when 
we distinguish the two meanings by using other suitable 
modes of expression it becomes apparent that the sup- 
posed syllogism contains four terms. The fallacy of 
equivocation may accordingly be considered a disguised 
fallacy of four terms. Thus if a person were to argue 
that " all criminal actions ought to be punished by law ; 
prosecutions for theft are criminal actions ; therefore 
prosecutions for theft ought to be punished by law," 
it is quite apparent that the term " criminal action" 
means totally different things in the two premises, and 
that there is no true middle term at all. Often, how- 
ever, the ambiguity is of a subtle and difficult character, 
so that different opinions may be held concerning it. 
Thus we might argue : 

"He who harms another should be punished. He 
who communicates an infectious disease to another per- 



164 FALLACIES. 

son harms him. Therefore he who communicates an 
infectious disease to another person should be pun- 
ished." 

This may or may not be held to be a correct argu- 
ment according to the kinds of actions we should con- 
sider to come under the term harm, according as we 
regard negligence or malice requisite to constitute harm. 
Many difficult legal questions are of this nature, as, for 
instance : 

Nuisances are punishable by law ; 

To keep a noisy dog is a nuisance; 

To keep a noisy dog is punishable by law. 

The question here would turn upon the degree of 
nuisance which the law would interfere to prevent. Or 
again : 

Interference with another man's business is illegal ; 

Underselling interferes with another man's business ; 
Therefore underselling is illegal. 

Here the question turns upon the hind of interference, 
and it is obvious that underselling is not the kind of 
interference referred to in the major premise. 

3. The Fallacy of Amphibology. 

The Fallacy of Amphibology consists in an ambiguous 
grammatical structure of a sentence, which produces 
misconception. A celebrated instance occurs in the 
prophecy of the spirit in Shakspeare's Henry VI. : 
" The Duke yet lives that Henry shall depose," which 
leaves it wholly doubtful whether the Duke shall depose 
Henry, or Henry the Duke. This prophecy is doubt- 
less an imitation of those which the ancient oracle of 



LOGICAL FALLACIES. 165 

Delphi is reported to have uttered ; and it seems that 
this fallacy was a great resource to the oracles who were 
not confident in their own powers of foresight. The 
Latin language gives great scope to misconstructions, 
because it does not require any fixed order for the words 
of a sentence, and when there are two accusative cases 
with an infinitive verb, it may be difficult to tell except 
from the context which comes in regard to sense before 
the verb. The double meaning which may be given to 
"twice two and three" arises from amphibology; it 
may be 7 or 10, according as we add the 3 after or be- 
fore multiplying. In the careless construction of sen- 
tences it is often impossible to tell to what part any 
adverb or qualifying clause refers. Thus, if a person 
says "I accomplished my business and returned the 
day after," it may be that the business was accomplished 
on the day after as well as the return; but it may 
equally have been finished on the previous day. Any 
ambiguity of this kind may generally be avoided by a 
simple change in the order of the words ; as for 
instance, " I accomplished my business, and, on the day 
after, returned." Amphibology may sometimes arise 
from confusing the subjects and predicates in a com- 
pound sentence, as if in "platinum and iron are very 
rare and useful metals," I were to apply the predicate 
useful to platinum and rare to iron, which is not 
intended. The word "respectively" is often used to 
show that the reader is not at liberty to apply each 
predicate to each subject. 

4. The Fallacy of Composition. 

The Fallacy of Composition is a special case of equivo- 
cation, arising from the confusion of an universal and a 



106 FALLACIES. 

collective term. In the premises of a syllogism we 
may- affirm something of a class of things distributively, 
that is, of each and any separately, and then we may in 
the conclusion infer the same of the whole put together. 
Thus we may say that "all the angles of a triangle are 
less than two right angles," meaning that any of the 
angles is less than two right angles ; but we must not 
infer that all the angles put together are less than two 
right angles. We must not argue that because every 
member of a jury is very likely to judge erroneously, 
the jury as a whole are also very likely to judge errone- 
ously ; nor that because each of the witnesses in a law 
case is liable to give false or mistaken evidence, no con- 
fidence can be reposed in the concurrent testimony of a 
number of witnesses. 

5. The Fallacy of Division. 

The Fallacy of Division is the converse of the pre- 
ceding, and consists in using the middle term collec- 
tively in the major premise, but distributively in the 
minor, so that the whole is divided into its parts. Thus 
it might be argued, "All the angles of a triangle are 
(together) equal to two right angles ; ABC is an angle 
of a triangle; therefore ABC is equal to two right 
angles." Or again, "The inhabitants of the town con- 
sist of men, women and children of all ages ; those 
who met in the Guildhall were inhabitants of the town ; 
therefore they consisted of men, women and children 
of all ages;" or, "The judges of the court of appeal 
cannot misinterpret the law ; Lord A. B. is a judge of 
the court of appeal ; therefore he cannot misinterpret 
the law." 



LOGICAL FALLACIES. . 167 

6, The Fallacy of Accent. 

The Fallacy of Accent consists in any ambiguity 
arising from a misplaced accent or emphasis thrown 
upon some word of a sentence. A ludicrous instance is 
liable to occur in reading Chapter XIII of the First 
Book of Kings, verse 27, where it is said of the prophet 
"And he spake to his sons, saying, Saddle me the ass. 
And they saddled Mm" The italics indicate that the 
word him was supplied by the translators of the author- 
ized version, but it may suggest a very different mean- 
ing. The Commandment " Thou shalt not bear false 
witness against thy neighbor" may be made by a 
slight emphasis of the voice on the last word to imply 
that we are at liberty to bear false witness against other 
persons. Mr. De Morgan, who remarks this, also points 
out that the erroneous quoting of an author, by unfairly 
separating a word from its context or italicising words 
which were not intended to be italicised, gives rise to 
cases of this fallacy. 

It is curious to observe how many and various may be the 
meanings attributable to the same sentence according as 
emphasis is thrown upon one word or another. Thus the sen- 
tence " The study of Logic is not supposed to communicate a 
knowledge of many useful facts," may be made to imply that the 
study of Logic does communicate such a knowledge, although it 
is not supposed to ; or that it communicates a knowledge of a, few 
useful facts ; or that it communicates a knowledge of many use- 
less facts. This ambiguity may be explained by considering that 
if you deny a thing to have the group of qualities A, B, C, D, 
the truth of your statement will be satisfied by any one quality 
being absent, and an accented pronunciation will often be used 
to indicate that which the speaker believes to be absent. If you 
deny that a particular fruit is ripe and sweet and well-flavored, 



168 FALLACIES. 

it may be unripe and sweet and well-flavored ; or ripe and sour 
and well-flavored ; or ripe and sweet and ill-flavored ; or any two 
or even all three qualities may be absent. But if you deny it to 
be ripe and sweet and well-flavored, the denial would be under- 
stood to refer to the last quality. Jeremy Bentham was so much 
afraid of being misled by this fallacy of accent that he employed 
a person to read to him, as I have heard, who had a peculiarly 
monotonous manner of reading. 

7, The Fallacy of the Figure of Speech. 

The Fallacy of the Figure of Speech is the sixth and 
last of the semi-logical fallacies, and is of a very trifling 
character. It appears to consist in any grammatical 
mistake or confusion between one part of speech and 
another. Aristotle gravely gives the following instance : 
" Whatever a man walks he tramples on ; a man walks 
the whole day ; therefore he tramples on the day." 
Here an adverbial phrase is converted into a noun 
object. 

In this Section, on "Logical Fallacies," we have 
considered :— 

1. The Classification of Logical Fallacies, 

2. The Fallacy of Equivocation. 

3. The Fallacy of Amphibology. 

4. The Fallacy of Composition. 

5. The Fallacy of Division. 

6. The Fallacy of Accent. 

7. The Fallacy of the Figure of Speech. 



MATERIAL FALLACIES. 169 



SECTION II, 

MATERIAL FALLACIES. 
1. The Classification of Material Fallacies. 

The Material fallacies are next to be considered ; and 
their importance is very great, although it is not easy 
to illustrate them by brief examples. There are alto- 
gether seven kinds of such fallacies enumerated by 
Aristotle and adopted by subsequent logicians, as fol- 
lows : 

1. The Fallacy of Accident. 

2. The Converse Fallacy of Accident. 

3. The Irrelevant Conclusion. 

4. The Petitio Principii. 

5. The Fallacy of the Consequent or Non sequitur. 

6. The False Cause. 

7. The Fallacy of Many Questions. 

2. The Fallacy of Accident and its Converse. 

Of -these the first two are conveniently described to- 
gether. The fallacy of accident consists in arguing 
erroneously from a general pule to a special case, where 
a certain accidental circumstance renders the rule inap- 
plicable. The converse fallacy consists in arguing from 
a special case to a general one. This latter fallacy is 
usually described by the Latin phrase a dicto secundum 
quid ad dictum simpliciter, meaning "from a state- 
ment under a condition to a statement simply or with- 
9 



170 FALLACIES. 

out that condition." Mr. De Morgan has remarked 
in his very interesting chapter on Fallacies* that 
we ought to add a third fallacy, which would con- 
sist in arguing from one special case to another special 
case. 

A few examples will illustrate these kinds of fallacy, 
but much difficulty is often encountered in saying to 
which of the three any particular example is best- 
referred. A most ancient example repeated in almost 
every logical hand-book is as follows: "What you 
bought yesterday you eat to-day ; you bought raw meat 
yesterday; therefore you eat raw meat to-day." The 
assertion in the conclusion is made of meat with the 
accidental quality of rawness added, where the first 
premise evidently speaks of the substance of the meat 
without regard to its accidental condition. This then 
is a case of the direct fallacy. If it is argued again 
that because wine acts as a poison when used in ex- 
cess it is always a poison, we fall into the converse 
fallacy. 

It would be a case of the direct fallacy of accident 
to infer that a magistrate is justified in using his power 
to forward his own religious views, because every man 
has a right to inculcate his own opinions. Evidently a 
magistrate as a man has the rights of other men, but in 
his capacity of a magistrate he is distinguished from 
other men, and he must not infer of his special powers 
in this respect what is only true of his rights as a 
man. For another instance take the following: " He 
who thrusts a knife into another person should be 

* Formal Logic, Chap. XIII. 



MATERIAL FALLACIES. 171 

punished; a surgeon in operating does so ; therefore he 
should be punished/' Though the fallacy of this is 
absurdly manifest, it is not so manifest how we are to 
classify the error. We may for instance say that as a 
general rule whoever stabs or cuts another is to be 
punished unless it can be shown to have been done 
under exceptional circumstances, as by a duly qualified 
surgeon acting for the good of the person. In this case 
the example belongs to the direct fallacy of accident. 
In another view we might interpret the first premise to 
mean the special case of thrusting a knife maliciously ; 
to argue from that to the case of a surgeon would 
be to infer from one special case to another special 
case. 

It is undoubtedly true that to give to beggars pro- 
motes mendicancy and causes evil ; but if we interpret 
this to mean that assistance is never to be given to 
those who solicit it, we fall into the converse fallacy of 
accident, inferring of all who solicit alms what is 
only true of those who solicit alms as a profession. 
Similarly it is a very good rule to avoid lawsuits 
and quarrels, but only as a general rule, since there 
frequently arise circumstances in which resort to the 
law is a plain duty. Almost all the difficulties which 
we meet in matters of law and moral duty arise from 
the impossibility of always ascertaining exactly to what 
cases a legal or moral rule does or does not extend ; 
hence the interminable differences of opinion, even 
among the judges of the land. 

3. The Fallacy of Irrelevant Conclusion. 

The Third Material Fallacy is that of the Irrelevant 



172 FALLACIES. 

Conclusion, technically called the Ignoratio Elenchi, or 

literally Ignorance of the Eefutation. It consists in 
arguing to the wrong point, or proving one thing in 
such a manner that it is supposed to be something else 
that is proved. Here again it would be difficult to 
adduce concise examples, because the fallacy usually 
occurs in the course of long harangues, where the 
multitude of words and figures leaves room for con- 
fusion of thought and forgetf ulness. This fallacy is in 
fact the great resource of those who have to support a 
weak case. It is not unknown in the legal profes- 
sion, and an attorney for the defendant in a lawsuit 
is said to have handed to the barrister his brief 
marked, "No case; abuse the plaintiff's attorney." 
Whoever thus uses what is known as argumentum 
ad hominem, that is an argument which rests, not 
upon the merit of the case, but the character or 
position of those engaged in it, commits this fallacy. 
If a man is accused of a crime it is no answer to 
say that the prosecutor is as bad. If a great change 
in the law is proposed in Parliament, it is an Irrele- 
vant Conclusion to argue that the proposer is not 
the right man to bring it forward. Every one who 
gives advice lays himself open to the retort that he 
who preaches ought to practise, or that those who live 
in glass houses ought not to throw stones. Never- 
theless there is no necessary connection between the 
character of the person giving advice and the goodness 
of the advice. 

The argumentum ad populum is another form of 
Irrelevant Conclusion, and consists in addressing argu- 
ments to a body of people calculated to excite their 



MATERIAL FALLACIES. 173 

feeling and prevent them from forming a dispassionate 
judgment upon the matter in hand. It is the great 
weapon of rhetoricians and demagogues. 

4. The Fallacy of Petitio Principii. 

Petitio Principii is a familiar name, and the nature of 
the fallacy it denotes is precisely expressed in the phrase 
begging the question. Another apt name for the fallacy 
is cir -cuius in pfobando, or "a circle in the proof." It 
consists in taking the conclusion itself as one of the 
premises of an argument. Of course the conclusion 
of a syllogism must always be contained or implied in 
the premises, but only when those premises are com- 
bined, and are distinctly different assertions from the 
conclusion. Thus in the syllogism, 

BkC, 
A\$B, 

therefore A is G, 

the conclusion is proved by being deduced from two 
propositions, neither of which is identical with it ; but 
if the truth of one of these premises itself depends 
upon the following syllogism, 

CisB, 

A is G, 

therefore A is B, 

it is plain that we attempt to prove a proposition by 
itself, which is as reasonable as attempting to support a 
body upon itself. It is not easy to illustrate this kind 
of fallacy by examples, because it usually occurs in 



174 FALLACIES. 

long arguments, and especially in wordy metaphysical 
writings. We are very likely to fall into it, however, 
when we employ a mixture of Saxon and Latin or 
Greek words, so as to appear to prove one proposition 
by another which is really the same expressed in differ- 
ent terms, as in the following: "Consciousness must 
be immediate cognition of an object ; for I cannot be 
said really to know a thing unless my mind has been 
affected by the thing itself." 

In the use of the disjunctive syllogism this fallacy is likely to 
happen ; for by enumerating only those alternatives which favor 
one view and forgetting the others it is easy to prove anything. 
An instance of this occurs in the celebrated sophism by which 
some of the ancient Greek Philosophers proved that motion was 
impossible. For, said they, a moving body must move either in 
the place where it is or the place where it is not ; now it is absurd 
that a body can be where it is not, and if it moves it cannot be in 
the place where it is ; therefore it cannot move at all. The 
error arises in the assumption of a premise which begs the ques- 
tion ; the fact of course is that the body moves between the place 
where it is at one moment and the place where it is at the next 
moment 

Jeremy Bentham, however, pointed out that the use even of a 
single name may imply a Petitio Principii. Thus in a Church 
asseinbly or synod, where a discussion is taking place as to 
whether a certain doctrine should be condemned, it would be a 
Petitio Principii to argue that the doctrine is heresy, and there- 
fore it ought to be condemned. To assert that it is heresy is to 
beg the question, because every one understands by heresy a 
doctrine which is to be condemned. Similarly in Parliament a 
bill is often opposed on the ground that it is unconstitutional and 
therefore ought to be rejected ; but as no precise definition can be 
given of what is or is not constitutional, it means little more than 
that the measure is distasteful to the opponent. Names which 
are used in this fallacious manner were aptly called by Bentham 



MATERIAL FALLACIES. 175 

Question-begging Epithets. In like manner we beg the ques- 
tion when we oppose any change by saying that it is un-English. 

5. The Fallacy of the Consequent. 

The Fallacy of the Consequent is better understood by 
the familiar phrase non sequitur. We may apply this 
name to any argument which is of so loose and incon- 
sequent a character that no one can discover any 
cogency in it. It thus amounts to little more than 
the assertion of a conclusion which has no connection 
with the premises. Professor De Morgan gives as an 
example the following: "Episcopacy is of Scripture 
origin; the Church of England is the only Episcopal 
Church in England; ergo, the Church established is 
the Church that should be supported." 

6. The Fallacy of False Cause, 

By the Fallacy of the False Cause I denote that 
which has generally been referred to by the Latin 
phrase non causa pro causd. In this fallacy we assume 
that one thing is the cause of another without any 
sufficient, grounds. A change in the weather is even 
yet attributed to the new moon or full moon which had 
occurred shortly before, although it has been demon- 
strated over and over again that the moon can have 
no such effect. In former centuries any plague or other 
public calamity which followed the appearance of a 
comet or an eclipse was considered to be the result 
of it. The Latin phrase post hoc ergo propter hoc 
(after this and therefore in consequence of this) exactly 
describes the character of these fallacious conclusions. 



176 FALLACIES. 

Though we no longer dread signs and omens, yet we 
often enough commit the fallacy ; as when we assume 
that all the prosperity of England is the result of the 
national character, forgetting that the plentiful coal in 
the country and its maritime position have contributed 
to the material wealth. It is no doubt equally falla- 
cious to attribute no importance to national character, 
and to argue that because England has in past centuries 
misgoverned Ireland all the present evils of Ireland are 
due to that misgovernment. 

7. The Fallacy of Many Questions. 

Lastly, there is the somewhat trivial Fallacy of Many 
Questions, which is committed by those who so combine 
two or three questions into one that no true answer can 
be given to them. I cannot think of a better example 
than the vulgar pleasantry of asking, " Have you left 
off beating your mother ? " Questions equally as unfair 
are constantly asked by barristers examining witnesses 
in a court of justice, and no one can properly be re- 
quired to answer Yes or No to every question which 
may be addressed to him. As Aristotle says, "Several 
questions put as one should be at once decomposed into 
their several parts. Only a single question admits of a 
single answer : so that neither several predicates of one 
subject, nor one predicate of several subjects, but only 
one predicate of one subject, ought to be affirmed or 
denied in a single answer." 

Read Professor De Morgan's excellent and amusing Chapter 

on Fallacies, Formal Logic, Chap. XIII. 
Whately's Remarks on Fallacies, Elements of Logic, Book III, 

are often very original and acute. 



MATERIAL FALLACIES. 177 

In this Section, on "Material Fallacies," we 
have considered : 

1. The Classification of Material Fallacies. 

2. The Fallacy of Accident and its Converse* 

3. The Fallacy of Irrelevant Conclusion, 

4. The Fallacy of Fetitio Frincipii, 

5. The Fallacy of the Consequent, 

6. The Fallacy of the False Cause, 

7. TheFallacy of Many Questions, 



CHAPTEH ¥♦ 

INDUCTION. 

The subject of Induction, as a process of inference, 
may be considered under the following divisions : (1) 
The Inductive Syllogism; (2) The Forms 
of Induction. 



SECTION I, 

THE INDUCTIVE SYLLOGISM. 

1. Induction and Deduction Contrasted. 

We have in previous chapters considered deductive 
reasoning, which consists in combining two or more 
general propositions synthetically, and thus arriving at 
a conclusion which is a proposition or truth of less 
generality than the premises, that is to say, it applies to 
fewer individual instances than the separate premises 
from which it was inferred. When I combine the 
general truth that "metals are good conductors of 
beat," with the truth that "aluminium is a metal," I 
am enabled by a syllogism in the mood Barbara to infer 
that "aluminium is a good conductor of heat." As 
this is a proposition concerning one metal only, it is 
evidently less general than the premise, which referred 
to all metals whatsoever. In induction, on the con- 



ustductiost. 179 

trary, we proceed from less general, or even from indi- 
vidual facts, to more general propositions, truths, or, as 
we shall often call them, Laws of Nature. When it is 
known that Mercury moves in an elliptic orbit round 
the Sun, as also Venus, the Earth, Mars, Jupiter, etc., 
we are able to arrive at the simple and general truth 
that " all the planets move in elliptic orbits round the 
sun." This is an example of an inductive process of 
reasoning. 

2, Explanation of Traduction. 

It is true that we may reason without rendering our 
conclusion either more or less general than the premises, 
as in the following : 

Snowdon is the highest mountain in England or Wales ; 
Snowdon is not so high as Ben Nevis ; 
Therefore the highest mountain in England or Wales is 
not so high as Ben Nevis. 

Again : 

Lithium is the lightest metal known ; 

Lithium is the metal indicated by one bright red line 
in the spectrum ; 

Therefore the lightest metal known is the metal .indi- 
cated by a spectrum of one bright red line. 

In these examples all the propositions are singular 
propositions, and merely assert the identity of singular 
terms, so that there is no alteration of generality. Each 
conclusion applies to just such an object as each of the 
premises applies to. To this kind of reasoning the apt 
name of Traduction has been given. 



180 INDUCTION. 

3. Importance of Induction. 

Induction is a much more difficult and more impor- 
tant kind of reasoning process than Traduction or even 
Deduction ; for it is engaged in detecting the general 
laws or uniformities, the relations of cause and effect, 
or in short all the general truths that may be asserted 
concerning the numberless and very diverse events that 
take place in the natural world around us. The greater 
part, and some philosophers think the whole, of our 
knowledge, is ultimately due to inductive reasoning. 
The mind, it is plausibly said, is not furnished with 
knowledge in the form of general propositions ready 
made and stamped upon it, but is endowed with powers 
of observation, comparison, and reasoning, which are 
adequate, when well educated and exercised, to procure 
knowledge of the world without us and the world within 
the human mind. Even when we argue synthetically 
and deductively from simple ideas and truths which 
seem to be ready in the mind, as in the case of the 
science of geometry, it may be that we have gathered 
those simple ideas and truths from previous observation 
or induction of an almost unconscious kind. This is a 
debated point upon which I will not here speak posi- 
tively; but if the truth be as stated, Induction will be 
the mode by which all the materials of knowledge are 
brought to the mind and analyzed. Deduction will 
then be the almost equally important process by which 
the knowledge thus acquired is utilized, and by which 
new inductions of a more complicated character, as we 
shall see, are rendered possible. 



INDUCTIVE SYLLOGISMS. 181 



4. Perfect and Imperfect Induction. 

An Induction, that is an act of Inductive reasoning, 
is called Perfect when all the possible cases or instances 
to which the conclusion can refer, have been examined 
and enumerated in the premises. If, as usually happens, 
it is impossible to examine all cases, since they may 
occur at future times or in distant parts of the earth or 
other regions of the universe, the Induction is called 
Imperfect. The assertion that all the months of the 
year are of less length than thirty-two days is derived 
from Perfect Induction, and is a certain conclusion 
because the calendar is a human institution, so that we 
know beyond doubt how many months there are, and 
can readily ascertain that each of them is less than 
thirty-two days in length. But the assertion that all 
the planets move in one direction round the sun, from 
West to East, is derived from Imperfect Induction ; for 
it is possible that there exist planets more distant than 
the most distant-known planet Neptune, and to such a 
planet of course the assertion would apply. 

5. The Difference between Perfect and Imper- 
fect Induction. 

It is obvious that there is a great difference between 
Perfect and Imperfect Induction. The latter includes 
some process by which we are enabled to make asser- 
tions concerning things that we have never seen or 
examined or even known to exist. But it must be care- 
fully remembered also that no Imperfect Induction can 
give a certain conclusion. It may be highly probable 
or nearly certain that the cases unexamined will re- 



1 82 INDUCTION. 

semble those which have been examined, bnt it can 
never be certain. It is quite possible, for instance, 
that a new planet might go round the sun in an opposite 
direction to the other planets. In the case of the satel- 
lites belonging to the planets more than one exception 
of this kind has been discovered, and mistakes have 
constantly occurred in science from expecting that all 
new cases would exactly resemble old ones. Imperfect 
Induction thus gives only a certain degree of proba- 
bility or likelihood that all instances will agree with 
those examined. Perfect Induction, on the other hand, 
gives a necessary and certain conclusion, but it asserts 
nothing beyond what was asserted in the premises. 

Mr. Mill, indeed, differs from almost all other logicians in hold- 
ing that Perfect Induction is improperly called Induction, because 
it does not lead to any new knowledge. He defines Induction as 
inference from the known to the unknown, and considers the unex- 
amined cases which are apparently brought into our knowledge 
as the only gain from the process of reasoning. Hence Perfect 
Induction seems to him to be of no scientific value whatever, be- 
cause the conclusion is a mere reassertion in a briefer form, a 
mere summing up of the premises. I may point out, however, 
that if Perfect Induction were no more than a process of abbre- 
viation it is yet of great importance, and requires to be continu- 
ally used in science and common life. Without it we could never 
make a comprehensive statement, but should be obliged to enu- 
merate every particular. After examining the books in a library 
and finding them to be all English books we should be unable 
to sum up our results in the one proposition, " all the books in 
this library are English books ; " but should be required to go 
over the list of books every time we desired to make any one 
acquainted with the contents of the library. The fact is, that 
the power of expressing a great number of particular facts in a 
very brief space is essential to the progress of science. Just as 
the whole science of arithmetic consists in nothing but a series of 



INDUCTIVE SYLLOGISM. 183 

processes for abbreviating addition and subtraction, and enabling 
us to deal vvitli a great number of units in a very sliort time, so 
Perfect Induction is absolutely necessary to enable us to deal 
with a great number of particular facts in a very brief space. 

6. The Perfect Inductive Syllogism. 

It is usual to represent Perfect Induction in the 
form of an Inductive Syllogism, as in the following 
instance : — 

Mercury, Venus, the Earth, etc., all move round the 

sun from West to East ; 
Mercury, Venus, the Earth, etc., are all the known 

Planets ; 
Therefore all the known planets move round the sun 

from West to East. 

This argument is a true Perfect Induction because 
the conclusion only makes an assertion of all knoivn 
planets, which excludes all reference to possible future 
discoveries ; and we may suppose that all the known 
planets have been enumerated in the premises. The 
form of the argument appears to be that of a syllogism 
in the third figure, namely Darapti, the middle term 
consisting in the group of the known planets. In 
reality, however, it is not an ordinary syllogism. The 
minor premise states not that Mercury, Venus, the 
Earth, Neptune, etc., are contained among the known 
planets, but that they are those planets, or are identi- 
cal with them. This premise is then a doubly uni- 
versal proposition of a kind not recognized in the Aris- 
totelian Syllogism. Accordingly we may observe that 
the conclusion is a universal proposition, which is not 
allowable in the third figure of the syllogism. 



184 INDUCTION - . 

As another example of a Perfect Induction we may 
take — 
January, February December, each contain less 

than 32 days. 

January December are all the months of the year. 

Therefore all the months of the year contain less than 

32 days. 

7. The Perfect Inductive Syllogism Disjunctive, 

Although Sir W. Hamilton has entirely rejected the 
notion, it seems worthy of inquiry whether the Induc- 
tive Syllogism be not really of the Disjunctive form of 
Syllogism. Thus I should be inclined to represent the 
last example in the form : 

A month of the year is either January, or February, 

or March or December ; but January has less 

than 32 days ; and February has less than 32 days ; and 
so on until we come to December, which has less than 
32 days. 

It follows clearly that a month must in any case have 
less than 32 days ; for there are only 12 possible cases, 
and in each case this is affirmed. The fact is that the 
major premise of the syllogism given above is a com- 
pound sentence with twelve subjects, and is there- 
fore equivalent to twelve distinct logical propositions. 
The minor premise is either a disjunctive proposition, 
as I have represented it, or something quite different 
from anything we have elsewhere had. 

8. The Imperfect Inductive Syllogism. 

From Perfect Induction we shall have to pass to 
Imperfect Induction ; but the opinions of Logicians are 



INDUCTIVE SYLLOGISM. 185 

not in agreement as to the grounds upon which we are 
warranted in taking a part of the instances only, and 
concluding that what is true of those is true of all. 
Thus if we adopt the example found in many books and 
say— 

This, that, and the other magnet attract iron ; 
This, that, and the other magnet are all magnets ; 
Therefore all magnets attract iron, 

we evidently employ a false minor premise, because this, 
that, and the other magnet which we have examined, 
cannot possibly be all existing magnets. In whatever 
form we put it there must be an assumption that the 
magnets which we have examined are a fair specimen 
of all magnets, so that what we find in some we may 
expect in all. Archbishop Whately considers that this 
assumption should be expressed in one of the premises, 
and he represents Induction as a Syllogism in Barbara 
as follows : 

That which belongs to this, that, and the other magnet, 

belongs to all ; 
Attracting iron belongs to this, that, and the other; 
Therefore it belongs to all. 

9. The Fundamental Assumption of Induction, 

But though the above is doubtless a correct expres- 
sion of the assumption made in an Imperfect Induc- 
tion, it does not in the least explain the grounds on 
which we are allowed to make the assumption, and 
under what circumstances such an assumption would 
be likely to prove true. Some writers have asserted 
that there is a Principle, called the Uniformity of Nature, 



186 INDUCTION. 

which enables us to affirm that what has often been 
found to be true of anything will continue to be found 
true of the same sort of thing. 

In his original work, and also in his " Principles of Science," 
Professor Jevons expresses his dissent from the doctrine of the 
Uniformity of Nature. This has led him into a controversy which 
it would be only perplexing to review in this connection, and the 
student is therefore referred below to the authorities who have 
most ably treated the subject. It is perhaps sufficient for the 
young learner to know that the truth of the doctrine of the 
Uniformity of Nature is essential to the validity of an Imperfect 
Induction. 

The advanced student may consult the following with advan- 
tage : 

Mansel's Aldrich, Appendix, Notes Gr and H. 

Hamilton's Lectures on Logic, Lecture XVII, and Appendix 

VII, On Induction and Example. 
J. S. Mill's System of Logic, Book III, Chap. 2, Of Inductions 

improperly so-called. Also, Jevon's Principles of Science, 

pp. 218, 229 ; and Fowler's Inductive Logic, Third Edition, 

pp. xi, xxiii. 

Iii this section, on " The Inductive Syllogism," 
we have considered :— 

1. Induction and Deduction Contrasted. 

2. The Explanation of Traduction. 

3. The Importance of Induction. 

4. Perfect and Imperfect Induction. 

5. The Difference betiveen Perfect and Imperfect 
Induction. 

6. The Perfect Inductive Syllogism. 

7. The Perfect Inductive Syllogism Disjunctive. 

8. The Imperfect Inductive Syllogism. 

9. The Fundamental Assumption of Induction. 



FORMS OF IKDUCTIOH. 187 



SECTION -XI. 

THE FORMS OF INDUCTION. 
1. The Character of the Data. 

It is now indispensable that we should consider with 
great care upon what grounds Imperfect Induction is 
founded. No difficulty is encountered in Perfect In- 
duction because all possible cases which can come 
under the general conclusion are enumerated in the 
premises, so that in fact there is no information in the 
conclusion which was not given in the premises. In 
this respect the Inductive Syllogism perfectly agrees 
with the general principles of deductive reasoning, 
which require that the information contained in the 
conclusion should be shown only from the data, and 
that we should merely unfold, or transform into an 
explicit statement what is contained in the premises 
implicitly. 

In Imperfect Induction the process seems to be of a 
wholly different character, since the instances concern- 
ing which we acquire knowledge may be infinitely more 
numerous than those from which we acquire the knowl- 
edge. 

(1) Geometrical Reasoning has a close resemblance 
to inductive reasoning. When in the fifth proposition 
of the first book of Euclid we prove that the angles at 
the base of an isosceles triangle are equal to each other, 
it is done by taking one particular triangle as an ex- 
ample. A figure is given which the reader is requested 



188 INDUCTION". 

to regard as having two equal sides, and it is conclu- 
sively proved that if the sides be really equal then the 
angles opposite to those sides must be equal also. But 
Euclid says nothing about other isosceles triangles ; he 
treats one single triangle as a sufficient specimen of all 
isosceles triangles, and we are asked to believe that 
what is true of that is true of any other, whether its 
sides be so small as to be only visible in a microscope, 
or so large as to reach to the furthest fixed star. There 
may evidently be an infinite number of isosceles tri- 
angles as regards the length of the equal sides, and each 
of these may be infinitely varied by increasing or 
diminishing the contained angle, so that the number of 
possible isosceles triangles is infinite ; and yet we are 
asked to believe of this incomprehensible number of 
objects what we have proved only of one single speci- 
men. This might seem to be the most extremely Im- 
perfect Induction possible, and yet every one allows 
that it gives us really certain knowledge. We do know 
with as much certainty as knowledge can possess, that 
if lines be conceived as drawn from the earth to two 
stars equally distant, they will make equal angles with 
the line joining those stars ; and yet we can never have 
tried the experiment. 

The generality of this geometrical reasoning evidently 
depends upon the certainty with which we know that 
all isosceles triangles exactly resemble each other. The 
proposition proved does not in fact apply to a triangle 
unless it agrees with our specimen in all the qualities 
essential to the proof. The absolute length of any of 
the sides or the absolute magnitude of the angle con- 
tained between any of them were not points upon which 



FORMS OF INDUCTION. 189 

the proof depended — they were purely accidental cir- 
cumstances ; hence we are at perfect liberty to apply to 
all new cases of an isosceles triangle what we learn of 
one case. 

Upon a similar ground rests all the vast body of certain knowl- 
edge contained in the mathematical sciences — not only all the 
geometrical truths, but all general algebraical truths. It was 
shown, for instance, in page 000, that if a and b be two quantities, 
and we multiply together their sum and difference, we get the 
difference of the squares of a and b. However often we try this 
it will be found true; thus if a=10 and b=7, the product of the 
sum and difference is 17 x 3=51 ; the squares of the quantities 
are 10 x 10 or 100 and 7 x 7 or 49, the difference of which is also 
51. But however often we tried the rule, no certainty would be 
added to it; because when proved algebraically there was no 
condition which restricted the result to any particular numbers, 
and a and b might consequently be any numbers whatever. This 
generality of algebraical reasoning by which a property is proved 
of infinite varieties of numbers at once, is one of the chief ad- 
vantages of algebra over arithmetic. 

(2) Mathematical Induction, or Demonstrative Induc- 
tion, is a process which shows the powers of reasoning 
in a very conspicuous way. A good example is found in 
the following problem : — If we take the first two con- 
secutive odd numbers, 1 and 3, and add them together, 
the sum is 4, or exactly twice two; if we take three 
such numbers 1+3 + 5, the sum is 9, or exactly three 
times three; if we take four, namely 1 + 3 + 5 + 7, the 
sum is 16, or exactly four times four ; or generally, if we 
take any given number of the series, 1 + 3 + 5 + 7+.. . 
the sum is equal to the number of the terms multiplied 
by itself. Any one who knows a very little algebra can 
prove that this remarkable law is universally true, as 



190 INDUCTION. 

follows : Let n be the number of terms, and assume for 
a moment that this law is true up to n terms, thus — 

1+3 + 5 + 7+.... +(8fi— l)=n\ 

Now add %n + 1 to each side of the equation. It fol- 
lows that — 

1 + 3 4-5 + 7+ +(2rc— l) + (2n + l)=n 2 + 2n + l. 

But the last quantity w 2 + 2w + l is just equal to 
(ft+1) 2 ; so that if the law is true for n terms it is true 
also for n-\-l terms. We are enabled to argue from 
each single case of the law to the next case ; but we 
have already shown that it is true of the first few cases, 
therefore it must be true of all. By no conceivable 
labor could a person ascertain by trial what is the sum 
of the first billion odd numbers, and yet symbolically 
or by general reasoning we know with certainty that 
they would amount to a billion billion, and neither 
more nor less even by a unit. This process of Mathe- 
matical Induction is not exactly the same as Geo- 
metrical Induction, because each case depends upon the 
last, but the proof rests upon an equally narrow basis 
of experience, and creates knowledge of equal certainty 
and generality. Such mathematical truths depend 
upon observation of a few cases, but they acquire cer- 
tainty from the perception we have of the exact similarity 
of one case to another, so that we undoubtingly believe 
what is true of one case to be true of another. 

(3) Uncertain Data. — It is very instructive to contrast 
with these cases certain other ones where there is a like 
ground of observation, but not the same tie of similarity. 
It was at one time believed that if any integral number 
were multiplied by itself, added to itself and then added 



FORMS OF INDUCTION. 191 

to 41, the result would be a prime number, that is a 
number which could not be divided by any other in- 
tegral number except unity ; in symbols, 

x % -j- x -f 41 = prime number. 

This was believed solely on the ground of trial and 
experience, and it certainly holds for a great many 
values of x. Thus, when x is successively made equal 
to the numbers in the first line below, the expression 
x 2 +x-\-41 gives the values in the second line, and they 
are all prime numbers : 

0123456789 10 
41 43 47 53 61 71 83 97 113 131 151 

No reason, however, could be given why it should 
always be true, and accordingly it is found that the 
rule does not always hold true, but fails when z=40. 
Then we have 40 x 40 + 40 + 41 =1681, but this is clearly 
equal to 41 x 40 + 41 or 41 x 41, and is not a prime 
number. 

In that branch of mathematics which treats of the peculiar 
properties and kinds of numbers, other propositions depending 
solely upon observation have been asserted to be always true. 

Thus Fermat believed that 2 2 + l always represents a prime 
number, but could not give any reason for the assertion. It 
holds true in fact until the product reaches the large number 
4294967297, which was found to be divisible by 641, so that the 
generality of the statement was disproved. 

We find then that in some cases a single instance 
proves a general and certain pule, while in others a very 
great number of instances are insufficient to give any 
certainty at all ; all depends upon the perception we 



192 INDUCTION. 

have of similarity or identity between one case and an- 
other. We can perceive no similarity between all prime 
numbers which assures us that because one is repre- 
sented by a certain formula, also another is; but we 
do find such similarity between the sums of odd num- 
bers, or between isosceles triangles. 

(4) Inductions in Physical Science Involve Exactly 
Similar Differences. — When a chemist analyzes a few 
grains of water and finds that they contain exactly 8 
parts of oxygen and 1 of hydrogen for 9 parts of water, 
he feels warranted in asserting that the same is true of 
all pure water whatever be its origin, and whatever be 
the part of the world from which it comes. But if he 
analyze a piece of granite, or a sample of sea-water from 
one part of the world, he does not feel any confidence 
that it will resemble exactly a piece of granite, or a 
sample of sea- water from another part of the earth; 
hence he does not venture to assert of all granite or 
sea-water, what he finds true of a single sample. Ex- 
tended experience shows that granite is very variable in 
composition, but that sea-water is rendered pretty uni- 
form by constant mixture of currents. Nothing but 
experience in these cases could inform us how far we 
may assert safely of one sample what we have ascertained 
of another. But we have reason to believe that chemi- 
cal compounds are naturally fixed and invariable in 
composition, according to Dalton's laws of combining 
proportions. No d priori reasoning from the principles 
of thought could have told us this, and we only learn 
it by extended experiment. But having once shown it 
to be true with certain substances we do not need to 
repeat the trial with all other substances, because we 



FORMS OF INDUCTION. 193 

have every reason to believe that it is a natural law in 
which all chemical substances resemble each other. It 
is only necessary then for a single accurate analysis of a 
given fixed compound to be made in order to inform 
us of the composition of all other portions of the same 
substance. 

It must be carefully observed, however, that all In- 
ductions in physical science are only probable, or that 
if certain, it is only hypothetical certainty they possess. 
Can I be absolutely certain that all water contains one 
part of hydrogen in nine ? I am certain only on two 
conditions : — 

1. That this was certainly the composition of the 
sample tried. 

2. That any other substance I call water exactly 
resembles that sample. 

But even if the first condition be undoubtedly true, I 
cannot be certain of the second. For how do I know 
what is water except by the fact of its being a trans- 
parent liquid, freezing into a solid and evaporating into 
steam, possessing a high specific heat, and a number of 
other distinct properties? But can I be absolutely cer- 
tain that every liquid possessing all these properties is 
water? Practically I can be certain, but theoretically 
I cannot. Two substances may have been created so 
like each other that we should never yet have discovered 
the difference ; we might then be constantly misled by 
assuming of the one what is only true of the other. 
That this should ever happen with substances possess- 
ing the very distinct qualities of water is excessively 
improbable, but so far is it from being impossible or 
improbable in other cases, that it has often happened. 
9 



194 INDUCTION. 

Most of the new elements discovered in late years have, with- 
out doubt, been mistaken previously for other elements. Caesium 
and Rubidium had been long mistaken for each other, and for 
Potassium, before they were distinguished by Bunsen and Kirch - 
hoff by means of the spectroscope. As they are now known to 
be widely distributed, although in small quantities, it is certain 
that what was supposed to be Potassium in many thousands of 
analyses was partly composed of different substances. Selenium 
had probably been confused with Sulphur, and there are certain 
metals — for instance, Rhodium, Ruthenium, Iridium, Osmium, 
and Beryllium — Yttrium, Erbium, Cerium, Lanthanum, and 
Didymium — Cadmium and Indium — which have only recently 
been distinguished. The progress of science will doubtless show 
that we are mistaken in many of our identifications, and various 
difficulties thus arising will ultimately be explained. 

(5) Future Phenomena. — Take again a very different 
case of induction. Are we certain that the sun will rise 
again to-morrow morning as it has risen for many 
thousand years, aud probably for some hundred million 
years ? We are certain only on this condition or hypo- 
thesis, that the planetary system proceeds to-morrow as 
it has proceeded for so long. Many causes may exist 
which might at any moment defeat all our calculations ; 
our sun is believed to be a variable star, and for what 
we know it might at any moment suddenly explode or 
flare up, as certain other stars have been observed to 
do, and we should then be all turned into thin lumi- 
nous vapor in a moment of time. It is not at all impos- 
sible that a collision did once occur in the planetary 
system, and that the minute planets or asteroids are the 
result. Even if there is no large meteor, comet or 
other body capable of breaking up the earth by colli- 
sion, yet it is probable that the sun moves through space 
at the rate of nearly 300 miles per minute, and if some 



FORMS OF INDUCTION. 195 

other star should meet us at a similar rate the 
consequences would be inconceivably terrible. It 
is highly improbable, however, that such an event 
should come to pass even in the course of a million 
years. 

(6) General Law from the Inspection of Data. — No 
mere Imperfect Induction can give certain knowledge ; 
all inference proceeds upon the assumption that new 
instances will exactly resemble old ones in all material 
circumstances; but in natural phenomena this is purely 
hypothetical, and we may constantly find ourselves in 
error. In Mathematical Induction certainty arose from 
the cases being hypothetical in their own nature, or 
being made so as exactly to correspond with the condi- 
tions. We cannot assert that any triangle existing in 
nature has two equal sides or two equal angles, and it 
is even impossible in practice that any two lines or 
angles can be absolutely equal. But it is nevertheless 
true that if the sides are equal the angles are equal. 
All certainty of inference is thus relative and hypothe- 
tical. Even in the syllogism the certainty of the con- 
clusion only rests on the hypothesis of certainty in 
the premises. It is probable, in fact, that all reason- 
ing reduces itself to a single type — that what is true of 
one thing will be true of another thing, on condition of 
there being an exact resemblance between them in all 
materia! circumstances. 

2. Special Kinds of Induction. 

There are two special varieties of Induction that 
deserve to be more particularly noticed : 
(1) Reasoning by Analogy. — In strictness an analogy 



196 INDUCTION. 

is not an identity of one thing with another, but an 
identity of relations. In the case of numbers 7 is not 
identical with 10 nor 14 with 20, but the ratio of 7 to 
10 is identical with the ratio of 14 to 20, so that there is 
an analogy between these numbers. To multiply two 
by two is not the same thing as to construct a square 
upon a line two units long ; but there is this analogy — 
that there will be just as many units of area in the 
square as there are units in the product of two by two. 
This analogy is so evident that we fearlessly assert a 
square mile to consist of 1760 x 1760 square yards with- 
out any trial of the truth. In ordinary language, how- 
ever, analogy has come to mean any resemblance be- 
tween things which enables us to believe of one what 
we know of the other. 

Thus the planet Mars possesses an atmosphere, with 
clouds and mist closely resembling our own ; it has seas 
distinguished from the land by a greenish color, and 
polar regions covered with snow. The red color of the 
planet seems to be due to the atmosphere, like the red 
color of our sunrises and sunsets. So much is similar 
in the surface of Mars and the surface of the Earth that 
we readily argue that there must be inhabitants there 
as here. All that we can certainly say, however, is, 
that if the circumstances be really similar, and similar 
germs of life have been created there as here, there 
must be inhabitants. The fact that many circum- 
stances are similar increases the probability. But be- 
tween the Earth and the Sun the analogy is of a much 
fainter character ; we speak indeed of the sun's, atmos- 
phere being subject to storms and filled with clouds, 
but these clouds are heated probably beyond the tern- 



FORMS OP INDUCTION. 197 

perature of our hottest furnaces ; if they produce rain 
it must resemble a shower of melted iron ; and the sun- 
spots are perturbations of so tremendous a size and 
character, that the earth together with half-a-dozen of 
the other planets could readily be swallowed up in one 
of them. It is plain then that there is little or no 
analogy between the Sun and the Earth, and we can 
therefore with difficulty form a conception of anything 
going on in a sun or star. 

Argument from analogy may be defined as direct inductive 
inference from one instance to any similar instance. It may, as 
Mr. Mill says, be reduced to the following formula : — 

" Two things resemble each other in one or more respects ; a 
certain proposition is true of the one ; therefore it is true of the 
other." This is no doubt the type of all reasoning, and the cer- 
tainty of the process depends entirely upon the degree of resem- 
blance or identity between the cases. In geometry the cases are 
absolutely identical in all material points by hypothesis, and no 
doubt attaches to the inference ; in physical science the identity 
is a question of probability, and the conclusion is in a like degree 
probable. ' It should be added that Mr. Mill considers Geometri- 
cal and Mathematical Induction not to be properly called Ind ac- 
tion, for reasons of which the force altogether escapes my appre- 
hension ; but the reader will find his opinions in the 2d chapter 
of the third book of his System of Logic. 

(2) Reasoning by Examples is a form of inductive 
inference consisting in the constant use of examples 
and instances. The best way to describe the nature of 
a class of things is to present one of the things itself, 
and point out the properties which belong to the class 
as distinguished from those peculiar to the thing. 
Throughout these lessons, as throughout every work 
on logic, instances of propositions, of compound or 



198 INDUCTION". 

complex sentences, of syllogisms, etc., are continually 
used, and the reader is asked to apply to all similar 
cases what he observes in the examples given. It is 
assumed that the writer selects such examples as truly 
exhibit the properties in question. 

While all inductive and analogical inferences rest upon the 
same principles there are wide differences between the sources of 
probability. In analogy we have two cases which resemble each 
other in a great many properties, and we infer that some addi- 
tional property in one is probably to be found in the other. The 
very narrow basis of experience is compensated by the high de- 
gree of similarity. In the processes more commonly treated under 
the name Induction, the things usually resemble each other only 
in two or three properties, and we require to have more instances 
to assure us that what is true of these is probably true of all 
similar instances. The less, in short, the intension of the resem- 
blance the greater must be the extension of our inquiries. 

Mr. Mill's System of Logic, Book III, Chap. XX. Of Analogy. 
Mansel's Aid/rich, App. Note H, On Example and Analogy. 

In this section, on "The Fornis of Induction," 
we have considered :— 

1. The CJiaracter of the Data, 

2. Special Kinds of Induction, 



CHAPTEB ¥!♦ 

METHOD. 

In the investigation and communication of truth, we 
may employ various modes of procedure, some of which 
must be better than others. Whatever mode we em- 
ploy is called our Method. This part of our subject is 
strictly Applied Logic, being little more than the appli- 
cation of the principles already discussed to the practi- 
cal cases of discovery and exposition. We shall con- 
sider Method in the following sections under these 
three topics: (1) Inductive Method; (2) De- 
ductive Method ; (3) Complete Method, 

The Inductive Method is sometimes called the Method of Dis- 
covery, and sometimes the Analytical Method. It begins with 
facts apparent to the powers of observation, and has the difficult 
task of detecting those universal laws or general principles which 
can only be comprehended by intellect. It has been aptly said 
that the method of discovery thus proceeds from tilings better 
known to us, or our senses (nobis notiora), to those which are more 
simple or better known in nature (notiora natural). The Deduc- 
tive Method, Method of Instruction, or Synthetic Method, pro- 
ceeds in the opposite direction, beginning with the things notiora 
naturce, and proceeding to show or explain the things nobis 
notiora. The difference is almost like that between hiding and 
seeking. He who has hidden a thing knows where to find it ; but 
this is not the position of a discoverer, who has no. clue except 
such as he may meet in his own diligent and sagacious search. 

It is very important indeed that the reader should clearly 
apprehend the meanings of Analysis and Synthesis. Analysis is 



200 METHOD. 

the process of separating a whole into its parts, and Synthesis 
the combination of parts into a whole. The analytical chemist, 
who receives a piece of mineral for examination, may be able to 
separate completely the several chemical elements of which it is 
composed and ascertain their nature and comparative quantities ; 
this is chemical analysis. In other cases the chemist mixes to- 
gether carefully weighed quantities of certain simple substances 
and combines them into a new compound substance ; this is 
chemical synthesis. Logical analysis and synthesis must not be 
confused with the physical actions, but they are nevertheless 
actions of mind of an analogous character. 

In logical synthesis we begin with the simplest possible 
notions or ideas, and combine them together. We have the best 
possible example in the elements of geometry. In Euclid we 
begin with certain simple notions of points, straight lines, 
angles, right angles, circles, etc. Putting together three straight 
lines we make a triangle; joining to this the notion of a right- 
angle, we form the notion of a right-angled triangle. Joining 
four other equal lines at right angles to each other we gain the 
idea of a square, and if we then conceive such a square to be 
formed upon each, of the sides of a right-angled triangle, and 
reason from the necessary qualities of these figures, we discover 
that the two squares upon the sides containing the right angle 
must together be exactly equal to the square upon the third side, 
as shown in the 47th Proposition of Euclid's first book. This is 
a perfect instance of combining simple ideas into more complex 
ones. 

We have often, however, in Geometry to pursue the opposite 
course of Analysis. A complicated geometrical figure may be 
given to us, and we may have, in order to prove the properties 
which it possesses, to resolve it into its separate parts, and to 
consider the properties of those parts each distinct from the 
others. 

To express the difference between knowledge derived deduc- 
tively and that obtained inductively, the Latin phrases d priori 
and d posteriori are often used. By A priori reasoning we mean 
argument based on truths previously known ; A posteriori rea- 
soning, on the contrary, proceeds to infer from the consequences 



INDUCTIVE METHOD. 201 

of a general truth what that general truth is. Many philosophers 
consider that the mind is naturally in possession of certain laws 
or truths which it must recognize in every act of thought ; all 
such, if they exist, would be d priori truths. It cannot be 
doubted, for instance, that we must always recognize in thought 
the three Primary Laws of Thought. We have there an a priori 
knowledge that " matter cannot both have weight and be without 
weight," or that "every thing must be either self-luminous or 
not self-luminous." But there is no law of thought which can 
oblige us to think that matter has weight, and luminous ether 
has not weight ; that Jupiter and Venus are not self-luminous, 
but that comets are to some extent self-luminous. These are 
facts which are no doubt necessary consequences of the laws of 
nature and the general constitution of the world ; but as we are 
not naturally acquainted with all the secrets of creation, we have 
to learn them by observation, or by the d posteriori method. 



SECTION I. 

INDUCTIVE METHOD. 

1. The Search for Facts. 

All knowledge, it may Be safely said, must be ulti- 
mately founded upon experience, which is but a general 
name for the various feelings impressed upon the mind 
at any period of its existence. The mind never creates 
entirely new knowledge independent of experience, and 
all that the reasoning powers can do is to arrive at the 
full meaning of the facts which are in our possession. 
In previous centuries men of the highest ability have 
held that the mind of its own power alone could, by 
sufficient cogitation, discover what things outside us 



202 METHOD. 

should be, and would be found to be on examination. 
They thought that we were able to anticipate Nature 
by evolving from the human mind an idea of what 
things would be made by the Creator. The celebrated 
philosopher Descartes thus held that whatever the 
mind can clearly conceive may be considered true ; but 
we can conceive the existence of mountains of gold or 
oceans of fresh water, which do not as a fact exist. 
Anything that we can clearly conceive must be con- 
formable to the laws of thought, and its existence is 
then not impossible, so far as our intellect is concerned ; 
but the forms and sizes and manners in which it has 
pleased the Creator to make things in this or any other 
part of the universe, cannot possibly be anticipated by 
the exceedingly limited wisdom of the human mind, 
and can only be learnt by actual examination of exist- 
ing things. 

In the latter part of the 13th century the great Roger Bacon 
clearly taught in England the supreme importance of experience 
as the basis of knowledge ; but the same doctrine was also, by a 
curious coincidence, again upheld in the 17th century by the 
great Chancellor Francis Bacon, after whom it has been called 
the Baconian Philosophy. I believe that Roger Bacon was even 
a greater man than Francis, whose fame is best known ; but the 
words in which Francis Bacon proclaimed the importance of 
experience and experiment must be ever memorable. In the 
beginning of his great work, the Novum Organ urn, or New In- 
strument, he thus points out our proper position as learners in 
the world of nature. 

"Man, the Servant and Interpreter of Nature, can do and 
understand as much as he has observed concerning the order of 
nature in outward things or in the mind ; more, he can neither 
know nor do." 

The above is the first of the aphorisms or paragraphs with 



INDUCTIVE METHOD. 203 

which the Novum Organum commences. In the second aphorism 
he asserts that the unaided mind can effect little and is liable to 
err ; assistance in the form of a definite logical method is requi- 
site, and this it was the purpose of his New Instrument to fur- 
nish. The 3d and 4th aphorisms must be given entire ; they 
are: — 

" Human science and human power coincide, because ignorance 
of a cause deprives us of the effect. For nature is not conquered 
except by obedience ; and what we discover as a cause by con- 
templation becomes a rule in operation." 

"Man can himself do nothing else than move natural bodies 
to or from each other ; nature working within accomplishes the 
rest. " 

Thus we see that the first essential in the inductive 
method is a knowledge of facts. This is obtained in 
two ways : 

(1) By Observation. — To observe is merely to notice 
events and changes which are produced in the ordinary 
course of nature, without being able, or at least attempt- 
ing, to control or vary those changes. Thus the early 
astronomers observed the motions of the sun, moon 
and planets among the fixed stars, and gradually de- 
tected many of the laws or periodical returns of those 
bodies. Thus it is that the meteorologist observes the 
ever-changing weather, and notes the height of the 
barometer, the temperature and moistness of the air, 
the direction and force of the wind, the height and 
character of the clouds, without being in the least able 
to govern any of these facts. The geologist again is 
generally a simple observer when he investigates the 
nature and position of rocks. The zoologist, the bota- 
nist, and the mineralogist usually employ mere observa- 
tion when they examine the animals, plants, and 



204 METHOD. 

minerals, as they are met with in their natural condi- 
tion. 

(2) By Experiment. — In experiment, on the contrary, 
we vary at our will the combinations of things and cir- 
cumstances, and then observe the result. It is thus 
that the chemist discovers the composition of water by 
using an electric current to separate its two constituents, 
oxygen and hydrogen. The mineralogist may employ 
experiment when he melts two or three substances 
together to ascertain how a particular mineral may 
have been produced. Even the botanist and zoologist 
are not confined to passive observation ; for by remov- 
ing animals or plants to different climates and different 
soils, and by what is called domestication, they may 
try how far the natural forms and species are capable 
of alteration. 

It is obvious that experiment is the most potent and 
direct mode of obtaining facts where it can be applied. 
We might have to wait years or centuries to meet 
accidentally with facts which we can readily produce at 
any moment in a laboratory ; and it is probable that 
most of the chemical substances now known, and many 
excessively useful products, would never have been dis- 
covered at all by waiting till nature presented them 
spontaneously to our observation. Many forces and 
changes too may go on in nature constantly, but in so 
slight a degree as to escape our senses, and render some 
experimental means necessary for their detection. Elec- 
tricity doubtless operates in every particle of matter, 
perhaps at every moment of time; and even the ancients 
could not but notice its action in the loadstone, in 
lightning, in the Aurora Borealis, or in a piece of 



INDUCTIVE METHOD. 205 

rubbed amber (electrum). But in lightning electricity 
was too intense and dangerous; in the other cases it 
was too feeble to be properly understood. The science 
of electricity and magnetism could only advance by 
getting regular supplies of electricity from the common 
electric machine or the galvanic battery, and by making 
powerful electro-magnets. Most if not all the effects 
which electricity produces must go on in nature, but 
altogether too obscurely for observation. 

Experiment, again, is rendered indispensable by the 
fact that on the surface of the earth we usually meet 
substances under certain uniform conditions, so that 
we could never learn by observation what would be the 
nature of such substances under other conditions. Thus 
carbonic acid is only met in the form of a gas, proceed- 
ing from the combustion of carbon ; but when exposed 
to extreme pressure and cold, it is condensed into a 
liquid, and may even be converted into a snow-like 
solid substance. Many other gases have in like manner 
been liquefied or solidified ; and there is reason to be- 
lieve that every substance is capable of taking all the 
three forms of solid, liquid and gas, if only the condi- 
tions of temperature and pressure can be sufficiently 
varied. Mere observation of nature would have led us, 
on the contrary, to suppose that nearly all substances 
were fixed in one condition only, and could not be con- 
verted from solid into liquid and from liquid into gas. 

It must not be supposed, however, that we can draw any pre- 
cise line between observation and experiment, and say where 
the one ends and the other begins. The difference is rather one 
of degree than of kind ; and all we can say is that the more we 
vary the conditions artificially the more we employ experiment. 



206 METHOD. 

I have said that meteorology is a science of nearly pure observa- 
tion, but if we purposely ascend mountains to observe the rare- 
faction and cooling of the atmosphere by elevation, or if we make 
balloon ascents for the same purpose, like Gay Lussac and 
Glaisher, we so vary the mode of observation as almost to render 
it experimental. Astronomers again may almost be said to ex- 
periment instead of merely observing when they simultaneously 
employ instruments as far to the north, and as far to the south, 
upon the earth's surface as possible, in order to observe the ap- 
parent difference of place of Venus when crossing the sun in a 
transit, so as thus to compare the distances of Venus and the sun 
with the dimensions of the earth. 

2. The Rule for Observation. 

Logic can give little or no aid in making an acute or 
accurate observer. There are no definite rules which 
can be laid down upon the subject. To observe well is 
an art which can only be acquired by practice and 
training ; and it is one of the greatest advantages of the 
pursuit of the Natural Sciences that the faculty of clear 
and steady observation is thereby cultivated. Logic 
can, however, give us this caution, which has been well 
pointed out by Mr. Mill— to discriminate accurately 
between what we really do observe and what we only 
infer from the facts observed. So long as we only 
record and describe what our senses have actually 
witnessed, we cannot commit an error ; but the moment 
we presume or infer anything we are liable to mistake. 
For instance, we examine the sun's surface with a tele- 
scope and observe that it is intensely bright except 
where there are small breaks or circular openings in 
the surface with a dark interior. We are irresistibly 
led to the conclusion that the inside of the sun is colder 
and darker than the outside, and record as a fact that 



INDUCTIVE METHOD. 207 

we saw the dark interior of the sun through certain 
openings in its luminous atmosphere. Such a record, 
however, would involve mistaken inference, for we saw 
nothing but dark spots, and we should not have done 
more in observation than record the shape, size, appear- 
ance and change of such spots. Whether they are dark 
clouds above the luminous surface, glimpses of the dark 
interior, or, as is now almost certainly inferred, something 
entirely different from either, can only be proved by a 
comparison of many unprejudiced observations. 

The reader cannot too often bear in mind the caution 
against confusing facts observed with inferences from 
those facts. It is not too much to say that nine-tenths 
of what we seem to see and hear is inferred, not really 
felt. Every sense possesses what are called acquired 
perceptions, that is, the power of judging unconsciously, 
by long experience, of many things which cannot be 
the objects of direct perception. The eye cannot see 
distance, yet we constantly imagine and say that we 
see things at such and such distances, unconscious that 
it is the result of judgment. As Mr. Mill remarks, it is 
too much to say "I saw my brother." All I positively 
know is that I saw some one who closely resembled my 
brother as far as could be observed. It is by judg- 
ment only I can assert he was my brother, and that 
judgment may possibly be wrong. 

Nothing is more important in observation and experi- 
ment than to be uninfluenced by any prejudice op theory 
in correctly recording the facts observed and allowing 
to them their proper weight. He who does not do so 
will almost always be able to obtain facts in support of 
an opinion however erroneous. 



208 METHOD. 



3. The Uses of Hypothesis and Theory. 

In order to carry on observation and experiment suc- 
cessfully, it is frequently necessary to form some hypo- 
thesis, or theory, to direct the course of inquiry. We 
will therefore notice these forms of supposition more 
particularly. 

(1) Hypothesis is derived from the Greek words vno, 
under, and deoig, placing, and is therefore exactly 
synonymous with the Latin word suppositio, a placing 
under, whence our common word supposition. It ap- 
pears to mean in science the imagining of some thing, 
force or cause, which underlies the phenomena we are 
examining, and is the agent in their production with- 
out being capable of direct observation. In making 
a hypothesis we assert the existence of a cause on the 
ground of the effects observed, and the probability 
of its existence depends upon the number of diverse 
facts or partial laws that we are thus enabled to ex- 
plain or reduce to harmony. To be of any value at all 
a hypothesis must harmonize at least two different 
facts. If we account for the effects of opium by saying 
with Moliere that it possesses a dormitive power, or say 
that the magnet attracts because it has a magnetic 
power, every one can see that we gain nothing. We 
know neither more nor less about the dormitive or 
magnetic power than we do about opium or the mag- 
net. But if we suppose the magnet to attract because 
it is occupied by circulating currents of electricity the 
hypothesis may seem a very improbable one, but is 
valid, because we thus draw a certain analogy between 
a magnet and a coil of wire conveying electricity. Such 



INDUCTIVE METHOD. 209 

a coil of wire attracts other coils exactly in the way that 
one magnet attracts another ; so that this hypothesis 
enables us to harmonize several different facts. The ex- 
istence of intense heat in the interior of the earth is hypo- 
thetical in so far as regards the impossibility of actually 
seeing and measuring the heat directly, but it harmo- 
nizes so many facts derived from different sources that 
we can hardly doubt its existence. Thus the occurrence 
of hot springs and volcanoes are some facts in its favor, 
though they might be explained on other grounds ; the 
empirical law that the heat increases as we sink mines 
in any part of the earth's surface is stronger evidence. 
The intensely heated condition of the sun and other 
stars is strongly confirmatory as showing that other 
bodies do exist in the supposed condition of the earth's 
interior. The cool state of the earth's surface is per- 
fectly consistent with its comparatively small size and 
the known facts and laws concerning the conduction 
and radiation of heat. And the more we learn con- 
cerning the way in which the sun's heat is supplied by 
the fall of meteoric matter, the more it is probable that 
the earth may have been intensely heated like the sun 
at some former time, although for an immense period 
it has been slowly growing colder. A supposition 
coinciding with so many facts, laws, and other probable 
hypotheses, almost ceases to be hypothetical, and its 
high probability causes it to be regarded as a known 
fact. 

Provided it is consistent with the laws of thought there is 
nothing that we may not have to accept as a probable hypothesis, 
however difficult it may be to conceive and understand. The 
force of gravity is hypothetical in so far that we know it only by 



210 METHOD. 

its effects upon the motions of bodies. Its decrease at a distance 
harmonizes exactly indeed with the way in which light, sound, 
electric or magnetic attractions, and in fact all influences which 
emanate from a point and spread through space, decrease ; hence 
it is probable that the law of the inverse square is absolutely 
true. But in other respects gravity is strongly opposed to all our 
ideas. If sound could travel to the sun as rapidly as in the 
earth's atmosphere it would require nearly fourteen years to 
reach its destination ; were the sun and earth united by a solid 
continuous bar of iron, a strong pull at one end would not be felt 
at the other until nearly three years had passed. Light indeed 
comes from the sun in rather more than eight minutes ; but what 
are we to think of the force of gravity, which appears to reach 
the sun in an instant — so short that no calculations have yet been 
able to detect any interval at all? In fact there seems some 
reason to suppose that gravity is felt instantaneously throughout 
the immeasurable regions of space. 

(2) The word Theory has constantly been used in the 
last few lessons, and deserves some examination. It 
comes from the Greek deupia, meaning contemplation, 
reflection or speculation ; but this gives us little clue to 
its modern use. In reality the word is highly am- 
biguous, being sometimes used as equivalent to hypo- 
thesis, at other times as equivalent to general law or 
truth. When people form theories concerning comets, 
the sun, the cause of earthquakes, etc., they imagine a 
great many things which may or may not exist ; such 
theories are really complicated hypotheses, and should 
be so called. In this sense there are two theories of 
electricity, one of which supposes the existence of a 
single fluid which accumulates in some places and has 
then a tendency to discharge itself towards places where 
there is a deficiency, just as water always tends to find 
its level ; the other supposes the existence of two fluids 



INDUCTIVE METHOD. 211 

which are commonly united, but when separated tend 
to rush back into union again. These so-called theories 
are really hypotheses, because we have no independent 
evidence of the existence of any fluid, and it is now 
almost certain that there is no such thing. The atomic 
theory, again, is really a hypothesis suggested by Dal- 
ton to explain the remarkable laws which he detected 
in the proportions of chemical elements which com- 
bine together. It is a valid hypothesis in so far 
as it does really explain the fixedness of the quantities 
which combine ; but it is purely hypothetical as regards 
the shapes, properties or absolute magnitudes of the 
atoms, because we have no facts which it can harmonize 
in these respects, and no apparent means of gaining 
them. 

In another and more proper sense theory is opposed 
to practice, just as the general is opposed to the par- 
ticular. The theory of gravitation means all the more 
general laws of motion and attraction on which New- 
ton founded his system of the Universe. "We may 
know what those laws are without being able to 
determine the place of a planet or make any prac- 
tical use of them ; the particular results must be 
calculated out by skilful astronomers before navi- 
gators, travellers or others can make practical use of 
them in the determination of the latitude or longi- 
tude. When we speak of the mathematical theory 
of sound, the lunar theory, the theory of the tides, 
the word is employed without any special reference 
to hypothesis, and is merely equivalent to general 
knowledge or science, implying the possession of a 
complete series of general and accurate laws, but in no 



212 METHOD. 

way distinguishing them from accurate knowledge in 
general. When a word is really used in an equivocal 
manner like theory, it is not desirable to attempt to 
give it an accurate definition which would be imagi- 
nary and artificial. 

4. Definitions of Terms Employed in 
Investigation. 

It is important that the learner should have precise 
ideas of the meaning of the following words employed 
in the investigation of truth, and accordingly these 
definitions are introduced at this point. 

(1) The word Fact is used very often in this as in 
most books, and demands a few remarks. It is derived 
from factum, the past participle of facere, to do, and 
would thus mean something ichicli is clone, an act, or 
deed ; but the meaning is evidently greatly extended by 
analogy. We usually oppose to each other fact and 
theory, but just as theory seems to have two ambiguous 
meanings, so I believe that fact is ambiguous. Some- 
times it means what is certain and known by the evi- 
dence of the senses, as opposed to what is known only 
probably by hypothesis and inference ; at other times it 
is contrasted to a general law, and is equivalent to a 
particular instance or case. A law of great generality 
may often be as certain and true, especially in mathe- 
matics, as the particular facts coming under it, so that 
the contrast must in this case be that between the 
general and particular. We often use the word too in 
common life, as merely equivalent to truth ; thus we 
might say, " It is a fact that the primary laws of 
thought are the foundation of reasoning." In short, as 



INDUCTIVE METHOD. 213 

theory means ambiguously what is hypothetical, general, 
abstract, or uncertain, so fact is equally ambiguous, 
and means confusedly what is intuitively known, par- 
ticular, concrete or certain. 

(2) The word Phenomenon will also be often used. 
It means simply anything tohich appears, and is there- 
fore observed by the senses ; the derivation of the 
word from the Greek word §aiv6\Lnvov, that which ap- 
pears, exactly corresponds to its logical use. 

(3) By the Cause of an event we mean the circum- 
stances which must have preceded in order that the 
event should happen. Nor is it generally possible to 
say that an event has one single cause and no more. 
There are usually many different things, conditions or 
circumstances necessary to the production of an effect, 
and all of them must be considered causes or necessary 
parts of the cause. Thus the cause of the loud explo- 
sion in a gun is not simply the pulling of the trigger, 
which is only the last apparent cause or occasion of the 
explosion ; the qualities of the powder, the proper form 
of the barrel, the existence of some resisting charge, 
the proper arrangement of the percussion cap and 
powder, the existence of a surrounding atmosphere, 
are among the circumstances necessary to the loud re- 
port of a gun ; any of them being ; absent it would not 
have occurred. 

(4) The learner will perhaps have noticed the fre- 
quent use of the word Tendency, and I have repeatedly 
spoken of a cause as tending to produce its effect. If 
the joint and homogeneous action of causes has been 
clearly explained, it will now be clear that a tendency 
means a cause which will produce an effect unless there 



114: METHOD. 

be opposite causes, which, in combination with it, 
counteract and disguise that effect. Thus when we 
throw a stone into the air the attractive power of the 
earth tends to make it fall, but the upward motion we 
have impressed upon it disguises the result for a certain 
time. The interminable revolving motion of the moon 
round the earth is the result of two balanced tendencies, 
that towards the earth, and that to proceed onward in 
a straight line. The laws of motion and gravity are 
such that this balance must always be preserved ; if the 
moon by any cause were brought nearer to the earth its 
tendency to fly off would be increased, and would ex- 
ceed the effect of gravity until it had regained its proper 
distance. A tendency then is a cause which may or 
may not be counteracted. 

(5) By an Antecedent we mean any thing, condition, 
or circumstance which 'exists before or, it maybe, at 
the same time with an event or phenomenon. By a 
Consequent we mean any thing, or circumstance, event, 
or phenomenon, which is different from any of the 
antecedents and follows after their conjunction or put- 
ting together. It does not follow that an antecedent is 
a cause, because the effect might have happened with- 
out it. Thus the sun's light may be an antecedent to 
the burning of a house, but not the cause, because the 
house would burn equally well in the night. A neces- 
sary or indispensable antecedent is, however, identical 
with a cause, being that without which the effect would 
not take place. 

(6) A Law is a uniform mode of sequence, or rule of 
action. The laws of nature are universal modes of 
sequence, or general expressions for the order of phe- 



INDUCTIVE METHOD. 215 

nomena. They are not causes, but the rules according 
to which causes act. 

5. Canons of Induction, 

Mr. Mill has laid down several rules, or canons, for 
the inductive determination of the laws of nature. 
These rules express certain methods of induction. 

(1) The first method of induction is that which Mr. 
Mill has aptly called the Method of agreement. It de- 
pends upon the rule that " If two or more instances of 
the phenomenon under investigation have only one cir- 
cumstance in common, the circumstance in which alone 
all the instances agree, is the cause (or effect) of the 
given phenomenon." The meaning of this First Canon 
of inductive inquiry might, I think, be more briefly 
expressed by saying that the sole invariable antecedent 
of a 'phenomenon is probably its cause. 

To apply this method we must collect as many in- 
stances of the phenomenon as possible, and compare 
together their antecedents. Among these the causes 
will lie, but if we notice that certain antecedents are 
present or absent without appearing to affect the result, 
we conclude that they cannot be necessary antecedents. 
Hence it is the one antecedent or group of antecedents 
always present, when the effect follows, that we con- 
sider the cause. For example, bright prismatic colors 
are seen on bubbles, on films of tar floating upon water, 
on thin plates of mica, as also on cracks in glass, or 
between two pieces of glass pressed together. On ex- 
amining all such cases they seem to agree in nothing 
but the presence of a very thin layer or plate, and it 
appears to make no appreciable difference of what kind 



216 METHOD. 

of matter, solid, liquid, or gaseous, the plate is made. 
Hence, we conclude that such colors are caused merely 
by the thinness of the plates, and this conclusion is 
proved true by the theory of the interference of light. 
Sir David Brewster beautifully proved in a similar way 
that the colors seen upon mother-of-pearl are not caused 
by the nature of the substance, but by the form of the 
surface. He took impressions of the mother-of-pearl 
in wax, and found that although the substance was 
entirely different the colors were exactly the same. 
And it was afterwards found that if a plate of metal 
had a surface marked by very fine close grooves, it 
would have iridescent colors like those of mother-of- 
pearl. Hence it is evident that the form of the sur- 
face, which is the only invariable antecedent or condi- 
tion requisite for the production of the colors, must be 
their cause. 

The method of agreement is subject to a serious difficulty, 
called by Mr. Mill the Plurality of Causes, consisting in the fact 
that the same effect may in different instances be owing to differ- 
ent causes. Thus if we inquire accurately into the cause of heat 
we find that it is produced by friction, by burning or combustion, 
by electricity, by pressure, etc.; so that it does not follow that if 
there happened to be one and the same thing present in all the 
cases we examined this would be the cause. 

(2) The second method of induction which we will 
now consider is free from this difficulty, and is known 
as the Method of Difference. It is stated in Mr. Mill's 
Second Canon as follows : — 

"If an instance in which the phenomenon under in- 
vestigation occurs, and an instance in which it does not 
occur, have every circumstance in common save one, 



INDUCTIVE METHOD. 217 

that one occurring only in the former, the circum- 
stance in which alone the two instances differ, is the 
effect, or the cause, or an indispensable part of the 
cause, of the phenomenon. " 

In other words, we may say that the antecedent which 
is invariably present when the phenomenon follows, 
and invariably absent when it is absent, other circum- 
stances remaining the same, is the cause of the phe- 
nomenon in those circumstances. 

Thus we can clearly prove that friction is one cause 
of heat, because when two sticks are rubbed together 
they become heated ; when not rubbed they do not be- 
come heated. Sir Humphrey Davy showed that even 
two pieces of ice when rubbed together in a vacuum 
produce heat, as shown by their melting, and thus com- 
pletely demonstrated that the friction is the source and 
cause of the heat. We prove that air is the cause of 
sound being communicated to our ears by striking a 
bell in the receiver of an air-pump, as Hawksbee first 
did in 1705, and then observing that when the receiver 
is full of air we hear the bell; when it contains little or 
no air we do not hear the bell. We learn that sodium 
or any of its compounds produces a spectrum having 
a bright yellow double line by noticing that there is no 
such line in the spectrum of light when sodium is not 
present, but that if the smallest quantity of sodium be 
thrown into the flame or other source of light, the 
bright yellow line instantly appears, Oxygen is the 
cause of respiration and life, because if an animal be 
put into a jar full of atmospheric air, from which the 
oxygen has been withdrawn, it soon becomes suffocated. 

This is essentially the great method of experiment, and its 
10 



218 METHOD. 

utility mainly depends upon the precaution of only varying one 
circumstance at a time, all other circumstances being maintained 
just as they were. This is expressed in one of the rules for con- 
ducting experiments given by Thomson and Tait in their great 
treatise on Natural Philosophy, Vol. I, p. 307, as follows : — 

" In all cases when a particular agent or cause is to be studied, 
experiments should be arranged in such a way as to lead if pos- 
sible to results depending on it alone ; or, if this cannot be done, 
they should be arranged so as to increase the effects due to the 
cause to be studied till these so far exceed the unavoidable con- 
comitants, that the latter may be considered as only disturbing, 
not essentially modifying, the effects of the principal agent." 

It would be an imperfect and unsatisfactory experiment to 
take air of which the oxygen has been converted into carbonic 
acid by the burning of carbon, and argue that, because an animal 
dies in such air, oxygen is the cause of respiration. Instead of 
merely withdrawing the oxygen we have a new substance, car- 
bonic acid, present, which is quite capable of killing the animal 
by its own poisonous properties. The animal, in fact, would be 
suffocated even when a considerable proportion of oxygen re- 
mained, so that the presence of the carbonic acid is a disturbing 
circumstance which confuses and vitiates the experiment. 

It is possible to prove the existence, and even to measure the 
amount of the force of gravity, by delicately suspending a small 
ball about the size of a marble and then suddenly bringing a very 
heavy leaden ball weighing a ton or more close to it, The small 
ball will be attracted and set in motion ; but the experiment 
would not be of the least value unless performed with the utmost 
precaution. It is obvious that the sudden motion of the large 
leaden ball would disturb the air, shake the room, cause currents 
in the air by its coldness or warmth, and even occasion electric 
attractions or repulsions ; and these would probably disturb the 
small ball far more than the force of gravitation. 

Beautiful instances of experiment according to this method are 
to be found, as Sir John Herschel has pointed out, in the re- 
searches by which Dr. Wells discovered the cause of dew. If on 
a clear calm night a sheet or other covering be stretched a foot 
or two above the earth, so as to screen the ground below from the 



INDUCTIVE METHOD. 219 

open sky, dew will be found on the grass around the screen but 
not beneath it. As the temperature and moistness of the air, ?.nd 
other circumstances, are exactly the same, the open sky must be 
an indispensable antecedent to dew. The same experiment is, 
indeed, tried for us by nature, for if we make observations of dew 
during two nights which differ in nothing but the absence of 
clouds in one and their presence in the other, we shall find that 
the clear open sky is requisite to the formation of dew. 

It may often happen that we cannot apply the method of differ- 
ence perfectly by varying only one circumstance at a time. Thus 
we cannot, generally speaking, try the qualities of the same sub- 
stance in the solid and liquid condition without any other change 
of circumstances, because it is necessary to alter the temperature 
of the substance in order to liquefy or solidify it. The tempera- 
ture might thus be the cause of what we attribute to the liquid 
or solid condition. Under such circumstances we have to resort 
to what Mr. Mill calls the joint method of agreement and differ- 
ence, which consists in a double application of the method of 
agreement, first to a number of instances where an effect is pro- 
duced, and secondly, to a number of quite different instances where 
the effect is not produced. It is clearly to be understood, however, 
that the negative instances differ in several circumstances from the 
positive ones ; for if they differed only in one circumstance we 
might apply the simple method of difference. Iceland spar, for 
instance, has a curious power of rendering things seen through 
it apparently double. This phenomenon, called double refraction, 
also belongs to many other crystals ; and we might at once prove 
it to be due to crystalline structure could we obtain any trans- 
parent substance crystallized and uncrystallized, but subject to no 
other alteration. We have, however, a pretty satisfactory proof 
by observing that uniform transparent uncrystallized substances 
agree in not possessing double refraction, and that crystalline 
substances, on the other hand, with certain exceptions which are 
easily explained, agree in possessing the power in question. 

(3) The principle of the Joint Method may be stated 

in the following rule, which is Mr. Mill's Third Canon : 

"If two or more instances in which the phenomenon 



220 METHOD. 

occurs have only one circumstance in common, while 
two or more instances in which it does not occur have 
nothing in common save the absence of that circum- 
stance ; the circumstance in which alone the two sets 
of instances (always or invariably) differ, is the effect, 
or the cause, or an indispensable part of the cause, of 
the phenomenon." 

I have inserted the words in parentheses, as without them the 
canon seems to me to express exactly the opposite of what Mr. 
Mill intends. 

It may facilitate the exact comprehension of these inductive 
methods if I give the following symbolic representation of them 
in the manner adopted by Mr. Mill. Let A, B, G, D, E, etc., 
be antecedents which may be variously combined, and let a, b, c, 
d, e, etc., be effects following from them. If then we can collect 
the following sets of antecedents and effects — 



Antecedents. 


Consequent! 


ABC 


dbc 


ABE 


ade 


AFG 


qfg 


AHE 


ahk 



we may apply the method of agreement, and little doubt will 
remain that A, the sole invariable antecedent, is the cause of a. 

The method of difference is sufficiently represented by- 
Antecedents. Consequents. 
ABC abc 
BG be 

Here while B and remain perfectly unaltered we find that the 
presence or absence of A occasions the presence or absence of a, 
of which it is therefore the cause, in the presence of B and C. 
But the reader may be cautioned against thinking that this proves 
A to be the cause of a under all circumstances whatever. 



INDUCTIVE METHOD. 221 

The joint method of agreement and difference is similarly 
represented by — 

Antecedents. Consequents. 
ABC dbe 

ABE ade 

AFG afg 

ARK ahk 

B8 rs 

TV tv 

XT xy 

Here the presence of A is followed as in the simple method of 
agreement by a ; and the absence of A, in circumstances differ- 
ing from the previous ones, is followed by the absence of a. 
Hence there is a very high probability that A is the cause of a. 
But it will easily be seen that A is not the only circumstance in 
which the two sets of instances differ, otherwise to any pair we 
might apply the simple method of difference. But the presence 
of A is a circumstance in which one set invariably, or uniformly, 
or always, differs, from the other set. This joint method is thus 
a substitute for the simpler method of difference in cases where 
that cannot be properly brought into action. 

(4) As soon as phenomena can be measured we can 
apply a further method of induction of a very important 
character. It is the method of difference indeed applied 
under far more favorable circumstances, where every 
degree and quantity of a phenomenon gives us a new 
experiment and proof of connection between cause and 
effect. It may be called the Method of Concomitant 
Variations, and is thus stated by Mr. Mill, in what he 
entitles the Fifth Canon of Induction : 

" Whatever phenomenon varies in any manner when- 



222 METHOD. 

ever another phenomenon varies in some particular 
manner, is either a cause or an effect of that phe- 
nomenon, or is connected with it through some fact 
of causation." 

Sir John Herschel's statement of the same method is 
as follows : — " Increase or diminution of the effect, with 
the increased or diminished intensity of the cause, in 
cases which admit of increase and diminution," to 
which he adds, "Keversal of the effect with that of 
the cause." 

The illustrations of this method are infinitely numer- 
ous. Thus Mr. Joule, of Manchester, conclusively 
proved that friction is a cause of heat by expending 
exact quantities of force in rubbing one substance 
against another, and showed that the heat produced 
was exactly greater or less, in proportion as the force 
was greater or less. We can apply the method to many 
cases which had previously been treated by the simple 
method of difference; thus instead of striking a bell in 
a complete vacuum we can strike it with a very little 
air in the receiver of the air-pump, and we then hear a 
very faint sound, which increases or decreases every 
time we increase or decrease the density of the air. 
This experiment conclusively satisfies any person that 
air is the cause of the transmission of sound. 

It is this method which often enables us to detect the 
material connection which exists between two bodies. 
For a long time it had been doubtful whether the red 
flames seen in total eclipses of the sun belonged to the 
sun or the moon ; but during the last eclipse of the 
sun it was noticed that the flames moved with the sun, 
and were gradually covered and uncovered by the moon 



IKDTJCTIVE METHOD. 223 

at successive instants of the eclipse. No one could 
doubt thenceforth that they belonged to the sun. 

Whenever, again, phenomena go through Periodic Changes, 
alternately increasing and decreasing, we should seek for other 
phenomena which go through changes in exactly the same 
periods, and there will probably be a connection of cause and 
effect. It is thus that the tides are proved to be due to the at- 
traction of the moon and sun, because the periods of high and 
low, spring and neap tides, succeed each other in intervals cor- 
responding to the apparent revolutions of those bodies round the 
earth. The fact that the moon revolves upon its own axis in 
exactly the same period that it revolves round the earth, so that 
for unknown ages past the same side of the moon has always 
been turned towards the earth, is a most perfect case of concomi- 
tant variations, conclusively proving that the earth's attraction 
governs the motions of the moon on its own axis. 

The most extraordinary case of variations, however, consists in 
the connection which has of late years been shown to exist be- 
tween the Aurora Borealis, magnetic storms, and the spots on the 
sun. It has only in the last 30 or 40 years become known that 
the magnetic compass needle is subject at intervals to very slight 
but curious movements ; and at the same time there are usually 
natural currents of electricity produced in telegraph wires so as 
to interfere with the transmission of messages. These disturb- 
ances are known as magnetic storms, and are often observed to 
occur when a fine display of the Northern or Southern Lights is 
taking place in some part of the earth. Observations during 
many years have shown that these storms come to their worst at 
the end of every eleven years, the maximum taking place about 
the present year, 1870, and then diminish in intensity until the 
next period of eleven years has passed. Close observations of 
the sun during 30 or 40 years have shown that the size and num- 
ber of the dark spots, which are gigantic storms going on upon 
the sun's surface, increase and decrease exactly at the same 
periods of time as the magnetic storms upon the earth's surface. 
No one can doubt, then, that these strange phenomena are con- 
nected together, though the mode of the connection is quite un- 



224 METHOD. 

known. It is now believed that the planets Jupiter, Saturn, 
Venus and Mars, are the real causes of the disturbances; for Bal- 
four Stewart and Warren de la Rue have shown that an exact 
correspondence exists between the motions of these planets and 
the periods of the sun-spots. This is a most remarkable and 
extensive case of concomitant variations. 

(5) We have now to consider a method of induction 
which must be employed when several causes act at 
once and their effects are all blended together, pro- 
ducing a joint effect of the same kind as the separate 
effects. If in one experiment friction, combustion, 
compression and electric action are all going on at once, 
each of these causes will produce quantities of heat 
which will be added together, and it will be difficult or 
impossible to say how much is due to each cause 
separately. We may call this a case of the homogeneous 
intermixture of effects, the name indicating that the 
joint effect is of the same kind as the separate effects. 
It is distinguished by Mr. Mill from cases of the hetero- 
geneous, or, as he says, the Jieteropathic intermixture 
of effects, where the joint effect is totally different in 
kind from the separate effects. Thus if we bend a bow 
too much it breaks instead of bending further ; if we 
warm ice it soon ceases to rise in temperature and 
melts ; if we warm water it rises in temperature homo- 
geneously for a time but then suddenly ceases, and an 
effect of a totally different kind, the production of 
vapor, or possibly an explosion, follows. 

Now when the joint effect is of a heterogeneous kind 
the method of difference is sufficient to ascertain the 
cause of its occurrence. Whether a bow or a spring 
will break with a given weight may easily be tried, and 



INDUCTIVE METHOD. 225 

whether water will boil at a given temperature in any- 
given state of the barometer may also be easily ascer- 
tained. But in the homogeneous intermixture of effects 
we have a more complicated task. There are several 
causes each producing a part of the effect, and we want 
to know how much is due to each. In this case we 
must employ a further inductive method, called by Mr. 
Mill the Method of Residues, and thus stated in his 
Fourth Canon : — 

"Subduct from any phenomenon such part as is 
known by previous inductions to be the effect of cer- 
tain antecedents, and the residue of the phenomenon is 
the effect of the remaining antecedents." 

If we know that the joint effect a, b, c is due to the 
causes A, B, and C, and can prove that a is due to A 
and b to B, it follows that c must be due to C. There 
cannot be a simpler case of this than ascertaining the 
exact weight of any commodity in a cart by weighing 
the cart and load, and then subtracting the tare or 
weight of the cart alone, which had been previously 
ascertained. We can thus too ascertain how much of 
the spring tides is due to the attraction of the sun, pro- 
vided we have previously determined the height of the 
tide due to the moon, which will be about the average 
height of the tides during the whole lunar month. 
Then subtracting the moon's tide the remainder is the 
sun's tide. 

Newton employed this method in a beautiful experiment to 
determine the elasticity of substances by allowing balls made of 
the substances to swing against each other, and then observing 
how far they rebounded compared with their original fall. But 
the loss of motion is due partly to imperfect elasticity and partly 



226 METHOD. 

to the resistance of the air. He determined the amount of the 
latter effect in the simplest manner by allowing the balls to 
swing without striking each other, and observing how much each 
vibration was less than the last. In this way he was enabled 
easily to calculate the quantity that must be subtracted for the 
resistance of the air. 

It is this method that we employ in making allowance for the 
errors or necessary corrections in observations. Few ther- 
mometers are quite correct ; but if we put a thermometer into 
melting snow, which has exactly the temperature of 0° Centi- 
grade, or 32° Fahr., we can observe exactly how much below or 
above the true point the mercury stands, and this will indicate 
how much we ought to add or subtract from readings of the 
thermometer to make them correct. The height of the barometer 
is affected by several causes besides the variation of the pressure 
of the air. It is decreased by the capillary repulsion between 
the glass tube and the mercury ; it is increased by the expansion 
of the mercury by heat, if the temperature be above 82° Fahr. ; 
and it may be increased or decreased by any error in the length 
of the measure employed to determine the height. In an accurate 
observation all these effects are calculated and allowed for in the 
final result. 

In all sciences which allow of measurement of quantities this 
method is employed, but more especially in astronomy, the most 
exact of all the sciences. Almost all the causes and effects in as- 
tronomy have been found out as residual phenomena, that is, by 
calculating the effects of all known attractions upon a planet or 
satellite, and then observing how far it is from the place thus pre- 
dicted. When this was very carefully done in the case of Uranus, 
it was still found that the planet was sometimes before and some- 
times behind its true place. This residual effect pointed to the 
existence of some cause of attraction not then known, but which 
was in consequence soon discovered in the shape of the planet 
Neptune. The motions of several comets have in this way been 
calculated, but it is observed that they return each time a little 
later than they ought. This retardation points to the existence 
of some obstructive power in the space passed through, the 
nature of which is not yet understood, 



DEDUCTIVE METHOD. 227 

The student is strongly recommended to read Sir J. Herscliel's 
Preliminary Discourse on the Study of Natural Philosophy 
(Lardner's Cabinet Cyclopaedia), especially Part II, Chaps. 4 
to 7, concerning Observation, Experiment, and the Inductive 
Processes generally ; Mill's System of Logic, Book III, Chaps. 
8, 10, 13 and 14. 

In this section, on "Inductive Method," we 
have considered: — 

1. The Search for Facts, 

2. The Mule for Observation, 

3. The Uses of Hypothesis and Theory 

4. Definitions of Terms Employed in Investi- 

gation; 

5. Canons of Induction, including ; 

(1) The Method of Agreement, 

(2) The Method of Difference, 

(3) The Joint Method, 

(4) The Method of Concomitant Variations, 

(5) The Method of Residues, 



SECTION II. 

DEDUCTIVE METHOD. 
1. The Predicables. 

There are certain logical terms known as predicables, 
meaning the kinds of terms or attributes which may 
always be predicated of any subject. Inasmuch as all 
truth known to man may be stated in the form of a 
proposition, it is important to know what these predi- 
cables are. They are five in number: genus, species, 
difference, property, and accident; and when properly 



228 METHOD. 

employed are of exceeding use and importance in logical 
science. It would neither be possible nor desirable in 
this work to attempt to give any idea of the various 
and subtle meanings which have been attributed to the 
predicables by ancient writers, and the most simple and 
useful view of the subject is what alone can be given 
here. 

(1) Any class of things may be called a genus (Greek 
yevog, race or kind), if it be regarded as made up of 
two or more species. "Element" is a genus when we 
consider it as divided into the two species "metallic 
and non-metallic." Triangle is a genus as regards the 
species acute-angled, right-angled, and obtuse-angled. 

(2) On the other hand, a species is any class which 
is regarded as forming part of the next larger class, so 
that the terms genus and species are relative to each 
other, the genus being the larger class which is divided, 
and the species the two or more smaller classes into 
which the genus is divided. 

(3) The difference may be defined as the quality or 
sum of qualities which mark out one part of a genus 
from the other part or parts. The difference (Latin 
differentia, Greek dcaQopd) cannot have any meaning 
except in intension ; and when we use all the terms 
wholly in intension we may say that the difference added 
to the genus makes the species. Thus, if " building" be 
the genus, and we add the difference " used for a dwell- 
ing," we get the species " house." If we take " triangle " 
as the genus, it means the sum of the qualities of 
"three-sided rectilineal figure;" if we add the quality 
of "having two sides equal," we obtain the species 
"isosceles triangle." 



DEDUCTIVE METHOD. 229 

It is indispensable, however, to regard these expressions in 
the double meaning of extension and intension. From the ex- 
planation of these different meanings in a previous chapter it 
will be apparent that the extent of a genus or species is simply 
the number of individuals included in it, and there will always 
be fewer individuals in the species than in the genus. In extent 
the genus book includes all books of whatever size, language, or 
contents ; if divided in respect to size the species of book are folio, 
quarto, octavo, duodecimo, etc ; and, of course, each of these species 
contains much fewer individual books than the whole genus. 

In intension the genus means, not the individual things con- 
tained in it, but the sum of the qualities common to all those 
things, and sufficient to mark them out clearly from other classes. 
The species similarly means the sum of the qualities common to 
all the individuals forming part of the genus, and sufficient to 
mark them out from the rest of the genus, as well as from all other 
things. It is evident, therefore, that there must be more qualities 
implied in the meaning of the species than of the genus, for the 
species must contain all the qualities of the genus, as well as a 
certain additional quality or qualities by which the several 
species are distinguished from each other. Now these additional 
qualities form the difference. 

It will easily be seen that the same class of things may be 
both a genus and a species at the same time, according as we re- 
gard it as divided into smaller classes or forming part of a larger 
class, Thus triangle, which is a genus as regards isosceles 
triangle, is a species as regards right-lined geometrical figures. 
House is a species of building, but a genus with respect to man- 
sion, cottage, villa, or other kinds of houses. We may, in fact, 
have an almost interminable chain of genera and species, each class 
being a species of the class next above it, and a genus as regards 
that next below. Thus the genus British subject has the species 
Born in the United Kingdom, Colonial-born, and Naturalized. 
Each of these becomes a genus as regards the species male and 
female ; each species again may be divided into adult and miuor, 
educated, uneducated, employed in some occupation or unem- 
ployed, self-maintaining, maintained by friends, or pauper ; and 
so on. The subdivision may thus proceed until we reach a class 



230 METHOD. 

of so restricted extent, that it cannot be divided except into 
individuals ; in this case the species is called the lowest species 
or infima species. All the intermediate genera and species of 
the chain are called subaltern (Latin sub, under, and alter, the 
other of two), because they stand one under the other. If there 
be a genus which is not regarded as a species, that is, as part of 
any higher genus, it is called the summum genus, the highest 
genus, or genus generalissimum, the most general genus. It is 
questionable whether we can thus set any limit to the chain of 
classes. The class British subject is certainly not an absolute 
summum genus, since it is but a species of man, which is a 
species of animal, living being, inhabitant of the earth, sub- 
stance, and so on. If there were any real summum genus it 
would probably be "Being," or "Thing," or "Object conceiv- 
able ; " but we may usefully employ the term to signify the 
highest class of things comprehended in any science or classifica- 
tion. Thus " material substance " is the summum genus examined 
in the science of chemistry ; " inhabitant of the United King- 
dom " is the summum genus enumerated and classified in the 
British census. Logical terms are only a species of words or 
phrases, but they are the summum genus as regards logic, which 
has nothing to do with the various parts of speech and the rela- 
tions of words, syllables, and letters, examined by grammarians. 

Several very useful expressions have been derived from the 
words genus and species. When a thing is so peculiar and un- 
like other things that it cannot easily be brought into one class 
with them, it is said to be sui generis, or of its own genus; thus 
the rings of Saturn are so different from anything else among 
the heavenly bodies that they may fairly be called sui generis. 
In zoology, the Ornithorhynchus, or Australian Duck-bill, the 
Amphioxus, and some other animals, are so peculiar that they 
may be called sui generis. When a substance is the same in all 
its parts, or when a number of things are all alike, we say that 
they are homogeneous (Greek bfibq, like, ykvoq, kind), that is, of the 
same nature ; otherwise they may be called heterogeneous (Greek 
erepog, other). 

It is necessary to distinguish carefully the purely logical use of 
the terms genus and species from their peculiar use in natural 



DEDUCTIVE METHOD. 231 

history. A species is there a class of plants and animals sup- 
posed to have descended from common parents, and to be the 
narrowest class possessing a fixed form ; the genus is the next 
higher class. But if we accept Darwin's theory of the origin of 
species, this definition of species becomes entirely illusory, since 
different genera and species must have according to this theory 
descended from common parents. The species then denotes a 
merely arbitrary amount of resemblance which naturalists choose 
to fix upon, and which it is not possible to define more exactly. 
This use of the term, then, has no connection whatever with the 
logical use, according to which any class of things whatever is a 
species, provided it is regarded as part of a wider class or genus. 

(4) The fourth of the Predi cables is Property (Latin 
proprium, Greek idiov, own), which it is hardly possible 
to define in a manner free from objection and difficulty, 
but which may perhaps be best described as any quality 
which is common to the whole of a class, but is not 
necessary to mark out that class from other classes. 
Thus it is a property of the genus " triangle" to have 
the three internal angles equal to two right angles ; this 
is a very remarkable circumstance, which is always 
true of triangles, but it is not made a part of the genus, 
or is not employed in defining a triangle, because the 
possession of three straight sides is a sufficient mark. 
The properties of geometrical figures are very numer- 
ous; the Second Book of Euclid is occupied in proving 
a few properties of rectangles; the Third Book simi- 
larly of circles. As we commonly use the term property 
it may or may not belong to other objects as well as 
those in question ; some of the properties of the circle 
may belong also to the ellipse ; some of the properties 
of man, as for instance the power of memory, or of 
anger, may belong to other animals. 



232 METHOD. 

Logicians have invented various subtle divisions of pro- 
perties, but it will be sufficient to say that a peculiar property is 
one which belongs to the whole of a class, and to that class only, 
as laughter is supposed to belong only to mankind ; the property 
of containing the greatest space in a line of given length is pecu- 
liar to circles. When a property is not peculiar, it may belong to 
other classes of objects as well as that of which it is called the 
property. We may further distinguish the Generic Property, or 
that which belongs to the whole of the genus, from the Specific 
Property, which belongs to the whole of a lowest species. 

(5) Lastly, an accident (Latin accidens, Greek ov[x(3e- 
Pr)n6g) is any quality which may indifferently belong or 
not belong to a class, as the case may be, without 
affecting the other qualities of the class. The word 
means that which falls or happens by chance, and has 
no necessary connection with the nature of a thing. 
Thus the absolute size of a triangle is a pure accident as 
regards its geometrical properties; for whether the side 
of a triangle be -fa of an inch or a million miles, what- 
ever Euclid proves to be true of one is true of the other. 
The birthplace of a man is an accident concerning him, 
as are also the clothes in which he is dressed, the posi- 
tion in which he rests, and so on. Some writers dis- 
tinguish separable and inseparable accidents. Thus 
the clothes in which a man is dressed is a separable 
accident, because they can be changed, as can also his 
position, and many other circumstances ; but his birth- 
place, his height, his Christian name, etc., are insepa- 
rable accidents, because they can never be changed, 
although they have no necessary or important relation 
to his general character. 

As an illustration of some part of the scheme of classification 
described under the name of Predicables, I may here give, as is 
usual in manuals of Logic, the Tree of Porphyry, a sort of ej- 



DEDUCTIVE METHOD. 



233 



ample of classification invented by one of the earliest Greek 
logicians, named Porphyrins. I have simplified the common 
form in which it is given by translating the Latin names and 
omitting superfluous words. 

In this Tree we observe a succession of genera and species — 
— Substance, Body, Living Being, Animal and Man. Of these, 
Substance is the summum genus, because it is not regarded as a 
species of any higher class ; Man is the infima species, because 
it is a class not divided into any lower class, but only into 
individuals, of whom it is usual to specify Socrates and Plato. 

Substance, 



Corporeal, 



Incorporeal, 



Body, 



Animate, 



Inanimate, 



Living Being, 



Sensible, 



Insensible, 






Rational, 



Animal, 



Man. 



Irrational, 



Socrates, Plato, and others. 

Body, Living Being, and Animal are called subaltern genera 



234 METHOD. 

and species, because each is a species as regards the next higher 
genus, and a genus as regards the next lower species. The 
qualities implied in the adjectives Corporeal, Animate, Sensible 
{i.e. capable of feeling) and Rational are the successive differences 
which occasion a division of each genus into species. It will 
be evident that the negative parts of the genera, namely Incor- 
poreal Substance, Inanimate Body, etc., are capable of sub- 
division, which lias not* been carried out in order to avoid 
confusing the figure. 

2. Logical Division. 

Logical division is the name of the process by which 
we distinguish the species of which a genus is composed. 
Thus we are said to divide the genus "book" when 
we consider it as made up of the groups folio, quarto, 
octavo, duodecimo books, etc., and the size of the books 
is in this case the ground, basis, or principle of divi- 
sion, commonly called the Fundamentum Divisionis. In 
order that a quality or circumstance may be taken as 
the basis of division, it must be present with some and 
absent with others, or must vary with the different 
species comprehended in the genus. A generic property 
of course, being present in the whole of the genus, can- 
not serve for the purpose of division. Three rules may 
be laid down to which a sound and useful division must 
conform : 

1. The constituent species must exclude each other. 

2. The constituent species must be equal when added 
together to the genus. 

3. The division must be founded upon one principle 
or basis. 

It would be obviously absurd to divide books into folio, quarto, 
French, German and dictionaries, because these species overlap 
each other, and there may be French or German dictionaries 
which, happen to be quarto or folio and belong to three different 



DEDUCTIVE METHOD. 235 

species at once. A division of this kind is said to be a Cross 
Division, because there is .more than one principle of division, 
and the several species in consequence cross each other and pro- 
duce confusion. If I were to divide rectilineal figures into tri- 
angles, parallelograms, rectangles and polygons of more than 
four sides, I should commit all the possible faults in one division. 
The species parallelogram and rectangle do not exclude each 
other, since all rectangles must be parallelograms ; the con- 
stituent species are not altogether equal to the genus rectilineal 
figure, since irregular four-sided figures which are not parallelo- 
grams have been omitted ; and there are three principles of divi- 
sion, namely the number of sides, the directions of those sides, 
and the angles contained. But when subdivision is employed, 
and each of the species is considered as a genus which may be 
subjected to a further separation, a new principle of division may 
and in fact must be employed each time. Thus I can divide 
rectilineal figures according to the three principles mentioned 
above : 

Rectilineal Figure 

3 sides 4 sides more than 4 sides 

Triangle Quadrilateral Polygon 

with parallel sides without parallel 

Parallelogram sides 

Trapezium. 

Here the principles of division are the number of their sides, 
and in the case of four-sided figures their parallelism. Triangles 
do not admit of division in this second respect. We may make a 
new division of parallelograms, adopting the equality of sides 
and the size of the angles as the principles ; thus : 
Parallelogram 



adjoining sides adjoining sides 

equal not equal 

I I 



! I I I 
right- not right- right- not right- 
angled angled angled angled 
Square Rhombus Oblong Rhomboid. 



236 METHOD. 

3. Dichotomy, or Exhaustive Division. 

The most perfect divisions in a logical point of view- 
are produced by continually dividing each genus into 
two species by a difference, of which an example has 
been given in the Tree of Porphyry. This process is 
called Dichotomy (Greek dixa, in two; refivo), to cut) ; 
it is also called Exhaustive Division because it always of 
necessity obeys the second rule, and provides a place 
for every possible existing thing. By a law of Thought 
considered in a previous chapter, every thing must 
either have a quality or not have it, so that it must fall 
into one or other division of the genus. This process 
of exhaustive division has considerable importance, but 
in practice it is not by any means always necessary or 
convenient. It would, for instance, produce a need- 
lessly long classification if we divided rectilineal figures 
thus: 

Eectilineal figure 

I I 
3-sided not 3-sided 
Triangle ! 

4-sided not 4-sided 



Quadrilateral 



5-sided not 5-sided 

Pentagon etc. 

As we know beyond all doubt that, every figure must 
have 3, 4, 5, 6, or more sides, and no figure can belong 
to more than one group, it is much better at once to 
enumerate the parts as Triangle, Quadrilateral, Penta- 
gon, Hexagon, etc. Again, it would be very awkward 
if we divided the counties of England into Middlesex 



DEDUCTIVE METHOD. 237 

and not-Middlesex ; the latter into Surrey and not- 
Surrey ; the latter, again, into Kent and not-Kent. Di- 
chotomy is useless, and even seems absurd in these cases, 
because we can observe the rules of division certainly in 
a much briefer division. But in less certain branches of 
knowledge our divisions can never be free from possible 
oversight unless they proceed by dichotomy. Thus, 
if we divide the population of the world into three 
branches, Aryan, Semitic, and Turanian, some race 
might ultimately be discovered which is distinct from 
any of these, and for which no place has been provided ; 
but had we proceeded thus — 

Man 

I 



I I . 

Aryan not- Aryan 



Semitic not-Semitic 



Turanian not Turanian, 

it is evident that the new race would fall into the last 
group, which is neither Aryan, Semitic, nor Turanian. 
All the divisions of naturalists are liable to this incon- 
venience. If we divide Vertebrate Animals into Mam- 
malia, Birds, Reptiles, and Fish, it may any time 
happen that a new form is discovered which belongs to 
none of these, and therefore upsets the division. 

A further precaution required in Division is not to proceed 
from a high or wide genus at once to a low or narrow species, or, 
as the phrase is, divisio nonfaciat saltum (the division should not 
make a leap). The species should always be those of the 
proximate or next higher genus ; thus it would obviously be 



238 METHOD. 

inconvenient to begin by dividing geometrical figures into those 
which have parallel sides and those which have not ; but this 
principle of division is very proper when applied to the proximate 
genus. 

Logical division must not be confused with physical division or 
Partition, by which an individual object, as a tree, is regarded as 
composed of its separate parts, root, trunk, branches, leaves, etc. 
There is even a third and distinct process, called Metaphysical 
Division, which consists in regarding a thing as an aggregate of 
qualities and separating these in thought ; as when we discrimi- 
nate the form, color, taste, and smell of an orange. 

4. Definition. 

Next to division the most important process of de- 
ductive method is Logical Definition, by which we 
determine the common qualities or marks of the objects 
belonging to any given class of objects. We must give 
in a definition the briefest possible statement of such 
qualities as are sufficient to distinguish the class from 
other classes, and determine its position in the general 
classification of conceptions. Now this will be fulfilled 
by regarding the class as a species, and giving the proxi- 
mate genus and the difference. The word genus is here 
used in its intensive meaning, and denotes the qualities 
belonging to all of the genus, and sufficient to mark 
them out ; and as the difference marks out the part of 
the genus in question; we get a perfect definition of the 
species desired. But we should be careful to give in a 
definition no superfluous marks ; if these are accidents 
and do not belong to the whole, the definition will be 
improperly narrowed, as if we were to define Quadri- 
lateral Figures as figures with four equal sides ; if the 
superfluous marks belong to all the things defined they 
are Properties, and have no effect upon the definition 



deductive method. 239 

whatever. Thus if I define parallelograms as "four- 
sided rectilineal figures, with the opposite sides equal 
and parallel, and the opposite angles equal," I have 
added two properties, the equality of the opposite sides 
and angles which necessarily follow from the parallelism 
of the sides, and only add to the complexity of the 
definition without rendering it more precise. 

There are certain pules usually given in logical 
works which express the precautions necessary in de- 
finition. 

1. A definition should state the essential attributes 
of the species defined. So far as any exact meaning 
can be given to the expression "essential attributes," 
it means, as explained above, the proximate genus and 
difference. 

2. A definition must not contain the name defined. 
For the purpose of the definition is to make the species 
known, and as long as it is not known it cannot serve 
to make itself known. When this rule is not observed, 
there is said to be " cir cuius in definiendo" or "a circle 
in defining," because the definition brings us round 
again to the very word from which we started. This 
fault will usually be committed by using a word in the 
definition which is really a synonym of the name de- 
fined, as if I were to define "Plant" as "an organized 
being possessing vegetable life," or elements as simple 
substances, vegetable being really equivalent to plant, 
and simple to elementary. If I were to define metals 
as "substances possessing metallic lustre," I should 
either commit this fault, or use the term metallic lustre 
in a sense which would admit other substances, and 
thus break the following rule. 



240 METHOD. 

3. A definition must be exactly equivalent to the 
species defined, that is to say, it must be an expression 
the denotation of which is neither narrower nor wider 
than the species, so as to include exactly the same ob- 
jects. The definition, in short, must denote the species, 
the whole species, and nothing but the species, and this 
may really be considered a description of what a defini- 
tion is. 

4. A definition must not be expressed in obscure, 
figurative, or ambiguous language. In other words, 
the terms employed in the definition must be all exactly 
known, otherwise the purpose of the definition, to make 
us acquainted with the sufficient marks of the species, 
is obviously defeated. There is no worse logical fault 
than to define ignotum per ignotius, the unknown by 
the still more unknown. Aristotle's definition of the 
soul as " The Entelechy, or first form of an organized 
body which has potential life," certainly seems subject 
to this objection. 

5. And lastly, A definition must not be negative where 
it can be affirmative. This rule, however, is often not 
applicable, and is by no means always binding. 

5. Classification. 

The joint use of division and definition is necessary 
in the important work of classification, so prominent 
in all scientific investigations. 

Classification may perhaps be best defined as the 
arrangement of things, or our notions of them, according 
to their resemblances or identities. Every class should 
be so constituted as to contain objects exactly resem- 
bling each other in certain definite qualities, which are 



DEDUCTIVE METHOD. 241 

stated in the definition of the class. The more numer- 
ous and extensive the resemblances which are thus 
indicated by any system of classes, the more perfect and 
useful must that system be considered. 

A collection of objects may generally be classified in 
an indefinite number of ways. Any quality which is 
possessed by some and not by others may be taken as 
the first difference, and the groups thus distinguished 
may be subdivided in succession by any other qualities 
taken at will. Thus a library of books might be 
arranged, (1) according to their size, (2) according to 
the language in which they are written, (3) according 
to the alphabetic order of their author's names, (4) 
according to their subjects; and in various other ways. 
In large libraries and in catalogues such modes of 
arrangement are adopted and variously combined. 
Each different arrangement presents some peculiar con- 
venience, and that mode must be selected which best 
meets the especial purpose of the library or catalogue. 
The population of a kingdom, again, may be classified 
in an almost endless number of ways with regard to 
different purposes or sciences. The population of the 
United Kingdom may be divided according to their 
place of birth, as English, Welsh, Scotch, Irish, colonial- 
born, and aliens. The ethnographer would divide them 
into Anglo-Saxons, Cymri, Gaels, Picts, Scandinavians, 
etc. The statist arranges them according to age; to 
condition, as married, unmarried, widowed, etc.; to 
state of body, as able, incapacitated, blind, imbecile. 
The political economist regards the innumerable trades 
which are carried on, and classifies them in a complex 
manner. The lawyer again treats every one as a minor, 
11 



242 METHOD. 

an adult, a feme sole, a feme couverte, a guardian, 
ward, trustee, felon, an . so on. 

The derivation of the word class is somewhat curious. In 
ancient Rome it was the practice to summon tlie whole people 
together at certain periods, and this ceremony was known as a 
cldsis, from the Greek K/Moig, or n/J/oir, derived from Kakku, to 
call together. Servius Tullius is said to have divided the people 
into six orders, according to the amount of tribute they could pay, 
and these orders were not unnaturally called the classes of the 
people. Hence the name came by degrees to be applied to any 
organized body of people, such as an army ; thence it was trans- 
ferred to a fleet of vessels as marshalled in a fixed order, and was 
finally extended by analogy to any collection of objects carefully 
arranged. When, however, we now speak of the lower or higher 
classes of the people it is curious that we are restoring the word 
very nearly to its original meaning. 

6. Requisites of a Good Classification. 

A good clarification has certain requisites, which 
may be named as follows : 

(1) The first requisite of a good classification is, that 
it shall be appropriate to the purpose in hand ; that is 
to say, the points of resemblance selected to form the 
leading classes shall be those of importance to the prac- 
tical use of the classification. All those things must be 
arranged together which require to be treated alike, 
and those things must be separated which require to be 
treated separately. Thus a lawyer has no need to classify 
persons according to the counties of England they were 
born in, because the law is the same independently of 
counties ; but so far as a Scotchman, a Manx man, or 
an alien, is under different laws from the English-born 
man, we shall require to classify them apart. A gar- 



DEDUCTIVE METHOD. 243 

dener is quite right in classifying plants as annuals, 
biennials, perennials; as herbs, shrubs, trees; as ever- 
green and deciduous ; or according to the soil, tempera- 
ture and other circumstances which affect them, because 
these are points which must guide him in treating 
some differently from others. 

(2) Another and, in a scientific point of view, the 
most important requisite of a good classification, is 
that it shall enable the greatest possible number of 
general assertions to be made. This is the criterion, 
as stated by Dr. Whewell, which distinguishes a natural 
from an artificial system of classification, and we must 
carefully dwell upon its meaning. It will be apparent 
that a good classification is more than a mere orderly 
arrangement ; it involves a process of induction which 
will bring to light all the more general relations which 
exist between the things classified. An arrangement 
of books will generally be artificial ; the octavo volumes 
will not have any common character except being of an 
octavo size. An alphabetical arrangement of names 
again is exceedingly appropriate and convenient to many 
purposes, but is artificial because it allows of few or no 
general assertions. We cannot make any general asser- 
tion whatever about persons because their names happen 
to begin with an A or a B, a P or a W. Even those 
who agree in bearing the name Smith or Taylor or 
Eobinson might be submitted to the inductive method 
of agreement without the discovery of any common 
circumstance which could be stated in a general propo- 
sition or law. It is true that if we investigated the 
antecedents of the Evanses and Joneses we should find 
them nearly all to be Welsh, and the Campbells to be 



244 METHOD. 

Scotch, and those who bear a very peculiar name would 
often be found to descend from common ancestors. So 
far even an alphabetic arrangement embodies some- 
thing that is natural in it, and enables general asser- 
tions to be made. Hardly any arrangement can be 
made, in fact, which will not indicate some vestiges of 
important relations and resemblances ; but what we 
want is a system which will reveal all the most impor- 
tant general truths. 

(3) For this purpose we must select as the ground of 
union those characters which carry with them most other 
characters. We have considered the proprium as a 
quality which belongs to the whole of a class without 
forming part of the definition of the class. Now we 
ought to frame the definition of a class that it may con- 
tain as few characters as possible, but that as many 
other characters, properties, or propria, as possible, 
shall be attributable to the things contained in the class. 
Every one can see, for instance, that animals form one 
great group of beings, which have many characters in 
common, and that plants form another group. Animals 
have sensation, voluntary motion, consume carbona- 
ceous food, and evolve carbonic acid, possess a stomach, 
and produce fat. Plants are devoid of sensation and 
voluntary motion, produce carbonaceous tissue, absorb 
carbonic acid, and evolve oxygen, possess no stomach, 
and produce starch. At one time it might have been 
thought that almost any of the characters named was a 
sufficient mark of the group to which a being belonged. 
Whatever had a stomach, was an animal; whatever 
had not, was a plant; whatever produced starch or 
evolved oxygen was called a plant ; whatever absorbed 



DEDUCTIVE METHOD. 245 

oxygen or produced fat was an animal. To the present 
day these statements remain generally true, so that we 
may make assertions in the form of the proposition U, 
that "all animals are all beings that evolve carbonic 
acid, and all plants are all beings that absorb carbonic 
acid." But in reality the exceptions are many, and 
increasing research makes it continually more apparent 
that there is no definite line to be drawn between 
animal and vegetable life. This, of course, is not a 
failure of logical science, but a fact of great significance 
concerning the things themselves. 

7. Denomination. 

In order to employ our results of classification, if not 
in the formation of classes, we need to name the pro- 
duct of our labors of division and definition. This 
process is Denomination. 

It is apparent that language serves three distinct and 
almost independent purposes : — 

1. As a means of communication. 

2. As a mechanical aid to thought. 

3. As an instrument of record and reference. 

In its first origin language was used chiefly if not 
exclusively for the first purpose. Savage tribes exist in 
great numbers at the present day who seem to accumu- 
late no knowledge. We may even say that the lower 
animals often possess some means of communication by 
sounds or natural signs which constitute language in 
the first sense, though they are incapable of reasoning 
by general notions. 

Some philosophers have held that it is impossible to 
carry on reasoning without the use of language. The 



246 METHOD. 

true nominalist went so far as to say that there are no 
such things as general notions, and that general names 
therefore constitute all that is general in science and 
reasoning. Though this is no doubt false, it must 
nevertheless be allowed that unless general ideas were 
fixed and represented by words, we could never attain 
to sustained thought such as we at present enjoy. The 
use of language in the second purpose is, doubtless, 
indispensable in a practical point of view, and reason- 
ing may almost be considered identical with the correct 
use of words. When language is used solely to assist 
reasoning there is no need that the meaning of each 
word should be fixed; we might use names, as the let- 
ters x, y, %, a, h, c, etc., are used in algebra to denote 
any quantity that happens to occur in a problem. All 
that is requisite is never to confuse the meaning attri- 
buted to a word in one argument with the different 
meaning attributed in another argument. Algebra 
may, in fact, be said to consist of a language of a very 
perfect kind adapted to the second purpose only, and 
capable of leading a person to the solution of a problem 
in a symbolical or mechanical manner. 

Language, as it is furnished to us ready made by the 
habitual growth of centuries, is capable of fulfilling all 
three purposes, though by no means in a perfect man- 
ner. As words possess a more or less fixed customary 
meaning we can not only reason by their aid, but com- 
municate our thoughts or record them ; and it is in 
this last respect we have now to treat the subject. 

The multitude of facts required for the establish- 
ment of a science could not be retained in the memory 
with sufficient accuracy. Hence an indispensable sub- 



DEDUCTIVE METHOD. ■ 247 

sidiary of reasoning is the means of describing and re- 
cording onr observations. Thus only can knowledge 
be accumulated, so that each observer shall start with 
the advantage of knowing what has been previously 
recorded and proved. It will be necessary then to con- 
sider the mode in which language serves for the regis- 
tration of facts, and to investigate the requisite quali- 
ties of a philosophical language suitable to the needs of 
science. 

As an instrument of record language must evidently 
possess two principal requisites : 

1. Precision or definiteness of meaning. 

2. Completeness. 

A name is worse than useless unless, when used to 
record a fact, it enables us to ascertain what was the 
nature of the fact recorded. Accuracy and precision is 
then a more important quality of language than abun- 
dance. The want of an appropriate word will seldom 
give rise to actual error and fallacy; it will merely 
oblige us to employ a circumlocutory phrase or else 
leave the fact unrecorded. But it is a self-evident con- 
venience that whenever a thing, notion, or quality has 
often to be referred to there should be a name appro- 
priated to the purpose, and there ought to be one 
name only. 

It may not previously have struck the learner, but it is certainly 
true, that description is impossible without the assertion of 
resemblance between the fact described and some other fact. 
We can describe a thing only by giving it a name ; but how can 
we learn the meaning of that name ? If we describe the name 
by other names we only have more names of which the meanings 
are required. We must ultimately learn the meanings, not from 
names, but from things which bear those names. If any one were 



248 METHOD. 

ignorant of the meaning of blue he could not be informed but by 
reference to something that excited in him the sensation of blue- 
ness, and had he been blind from birth he could not acquire any 
notion of what blueness was. There are, indeed, a number of 
words so familiar to us from childhood that we cannot tell when 
or how we learnt their meanings, though it must have been by 
reference to things. But when we come to the more precise use 
of names we soon have to make fresh reference to physical ob- 
jects. Then we should describe the several kinds of blue color 
as sky-blue, azure-blue, indigo-blue, cobalt-blue ; green color we 
likewise distinguish as sea-green, olive-green, emerald-green, 
grass-green, etc. The shapes of leaves are described in Botany 
by such names as ovate, lanceolate, linear, pinnate, peltate, refer- 
ring the mind respectively to an egg, a lance, a line, a feather, 
and a shield. In recording dimensions it is equally impossible 
to avoid comparison with the dimensions of other things. A 
yard or a foot has no meaning unless there be a definite standard 
yard or foot which fixes its meaning; and the learner is prob- 
ably aware that when the physical standard of a length is once 
completely lost it can never be recovered. The word is nothing 
unless we somewhere have the thing to which it corresponds. 

See Dr. Whewell's "Aphorisms concerning the Language of 
Science," at the end of his Philosophy of the Inductive 
Sciences. 

Thomson's Outline of the Laws of Thought, contains most 
interesting remarks on the general nature and use of Lan- 
guage, Sections 17-31. 

In this section, on "Deductive Method," we 
have considered :— 

1 . The Predicables. 

2. Logical Division, 

3. Dichotomy, or Exhaustive Division. 

4. Definition. 

5. Classification. 

6. Requisites of a Good Classification, 

7. Denomination. 



COMPLETE METHOD. 249 



SECTION III. 

COMPLETE METHOD. 
1. Empirical and Rational Knowledge. 

When a law of nature is ascertained purely by in- 
duction from certain observations or experiments, and 
has no other guarantee for its truth, it is said to be an 
empirical law. As Mr. Mill says, " Scientific inquirers 
give the name of Empirical Laws to uniformities which 
observation or experiment has shown to exist, but on 
which they hesitate to rely in cases varying much from 
those which have been actually observed, for want of 
seeing any reason why such a law should exist." The 
name is derived from the Greek word epireipia, meaning 
experience or trial. Instances of such laws are abun- 
dant. We learn empirically that a certain strong yellow 
color at sunset, or an unusual clearness in the air, por- 
tends rain ; that a quick pulse indicates fever ; that 
horned animals are always ruminants; that quinine 
affects beneficially the nervous system and the health of 
the body generally ; that strychnine has a terrible effect 
of the opposite nature : all these are known to be true 
by repeated observation, but we can give no other rea- 
son for their being true, that is, we cannot bring them 
into harmony with any other scientific facts ; nor could 
we at all have deduced them or anticipated them on the 
ground of previous knowledge. The connection be- 
tween the sun's spots, magnetic storms, auroras, and 
the motions of the planets mentioned in the last lesson, 
is perhaps the most remarkable known instance of an 



250 METHOD. 

empirical induction ; for no hint has yet heen given of 
the way in which these magnetic influences are exerted 
throughout the vast dimensions of the planetary system. 
The qualities of the several alloys of metals are also 
good instances of empirical knowledge. No one can 
tell before mixing two or three metals for the first time 
in any given proportions what the qualities of the mix- 
ture will be — that brass should be both harder and more 
ductile than either of its constituents, copper and zinc ; 
that copper alloyed with the very soft metal tin should 
make hard and sonorous bell-metal ; that a certain mix- 
ture of lead, bismuth, tin and cadmium, should melt 
with a temperature (65° cent.) far below that of boiling 
water. , 

However useful may be empirical knowledge, it is yet 
of slight importance compared with the well-connected 
and perfectly explained body of knowledge which con- 
stitutes an advanced and deductive science. It is in 
fact in proportion as a science becomes deductive, and 
enables us to grasp more and more apparently uncon- 
nected facts under the same law, that it becomes per- 
fect. He who knows exactly why a thing happens, will 
also know exactly in what cases it will happen, and 
what difference in the circumstances will prevent the 
event from happening. Take for instance the simple 
effect of hot water in cracking glass. This is usually 
learnt empirically. Most people have a confused idea 
that hot water has a natural and inevitable tendency to 
break glass, and that thin glass, being more fragile than 
other glass, will be more easily broken by hot water. 
Physical science, however, gives a very clear reason for 
the effect, by showing that it is only one case of the 



COMPLETE METHOD. 251 

general tendency of heat to expand substances. The 
crack is caused by the successful effort of the heated 
glass to expand in spite of the colder glass with which 
it is connected. But then we shall see at once that the 
same will not be true of thin glass vessels ; the heat 
will pass so quickly through that the glass will be nearly 
equally heated ; and accordingly chemists habitually 
use thin uniform glass vessels to hold or boil hot liquids 
without fear of the fractures which would be sure to 
take place in thick glass vessels or bottles. 

We have hitherto treated of Deduction and Induction as if they 
were entirely separate and independent methods. In reality they 
are frequently blended or employed alternately in the pursuit of 
truth ; and it may be said that all the more important and exten- 
sive investigations of science rely upon one as much as upon the 
other. It is probably the greatest merit in Mr. Mill's logical 
writings that he points out the entire insufficiency of what is 
called the Baconian Method to detect the more obscure and 
difficult laws of nature. Bacon advised that we should always 
begin by collecting facts, classifying them according to their 
agreement and difference, and gradually gathering from them 
laws of greater and greater generality. He protested altogether 
against ' ' anticipating nature," that is, forming our own hypoth- 
eses and theories as to what the laws of nature probably are, and 
he seemed to think that systematic arrangement of facts would 
take the place of all other methods. The learner will soon see 
that the progress of Science has not confirmed his opinions. 

2. The Elements of Complete Method. 

Combined or Complete Method, consists in the alter- 
nate use of induction and deduction. It may be said 
to have three steps, as follows : — 

1. Direct Induction. 



252 METHOD. 

2. Deduction, or, as Mr. Mill calls it, Ratiocination. 

3. Verification. 

The first process consists in such a rough and simple 
appeal to experience as may give us a glimpse of the 
laws which operate, without being sufficient to establish 
their truth. Assuming them as provisionally true, we 
then proceed to argue to their effects in other cases, and 
a further appeal to experience either verifies or negatives 
the truth of the laws assumed. There are, in short, 
two appeals to experience connected by the intermediate 
use of reasoning. Newton, for instance, having passed a 
ray of sun-light through a glass prism found that it 
was spread out into a series of colors resembling those 
of the rainbow. He adopted the theory that white 
light was actually composed of a mixture of different 
colored lights, which become separated in passing 
through the prism. He saw that if this were true, and 
he were to pass an isolated ray of the spectrum, for 
instance, the yellow ray, through a second prism, it 
ought not to be again broken up into different colors, 
but should remain yellow whatever was afterwards done 
with it. On trial he found this to be the case, and 
afterwards devised a succession of similar confirmatory 
experiments which verified his theory beyond all pos- 
sible doubt. 

The greatest result of the complete method is no less than the 
theory of gravitation, which makes a perfect instance of its 
procedure. In this case the preliminary induction consisted, we 
may suppose, in the celebrated fall of the apple, which occurred 
while Newton was sitting in an orchard during his retirement 
from London, on account of the Great Plague. The fall of the 
apple, we are told, led Newton to reflect that there must be a 



COMPLETE METHOD. 253 

power tending to draw bodies towards the earth, and he asked 
himself the question why the moon did not on that account fall 
upon the earth. The Lancashire astronomer Horrocks suggested 
to his mind another fact, namely, that when a stone is whirled 
round attached to a string, it exerts a force upon the string, often 
called centrifugal force. Horrocks remarked that the planets in 
revolving round the sun must tend in a similar way to fly off 
from the centre. Newton was acquainted with Horrocks' views, 
and was thus possibly led to suppose that the earth's attractive 
force might exactly neutralize the moon's centrifugal tendency, 
so as to maintain that satellite in constant rotation. 

But it happened that the world was in possession of certain 
empirical laws concerning the motions of the planets, without 
which Newton could scarcely have proceeded further. Kepler 
had passed a lifetime in observing the heavenly bodies, and 
forming hypotheses to explain their motions. In general his 
ideas were wild and unfounded, but the labors of a lifetime were 
rewarded in the establishment of the three laws which bear his 
name, and describe the nature of the orbits traversed by the 
planets, and the relation between the size of such orbit and the 
time required by the planet to traverse it. Newton was able to 
show by geometrical reasoning that if one body revolved round 
another attracted towards it by a force decreasing as the square 
of the distance increases, it would necessarily describe an orbit 
of which Kepler's laws would be true, and which would there- 
fore exactly resemble the orbits of the planets. Here was a 
partial verification of his theory by appeal to the results of ex- 
perience. But several other philosophers had gone so far in the 
investigation of the subject. It is Newton's chief claim to 
honor, that he carried on his deductions and verifications until he 
attained complete demonstration. To do this it was necessary 
first of all to show that the moon actually does fall towards the 
earth just as rapidly as a stone would if it were in the same cir- 
cumstances. Using the best information then attainable as to the 
distance of the moon, Newton calculated that the moon falls 
through the space of 13 feet in one minute, but that a stone, if 
elevated so high, would fall through 15 feet. Most men would 
have considered this approach to coincidence as a proof of his 



254 , METHOD. 

theory, but Newton's love of certain truth rendered him different 
even from most philosophers, and the discrepancy caused him to 
lay " aside at that time any further thoughts of this matter." 

It was not till many years afterwards (probably 15 or 16) that 
Newton, hearing of some more exact data from which he could 
calculate the distance of the moon, was able to explain the dis- 
crepancy. His theory of gravitation was then verified so far as the 
moon was concerned ; but this was to him only the beginning of a 
long course of deductive calculations, each ending in a verification, 
If the earth and moon attract each other, and also the sun and the 
earth, similarly there is no reason why the sun and moon should 
not attract each other. Newton followed out the consequences 
of this inference, and showed that the moon would not move as 
if attracted by the earth only, but sometimes faster and some- 
times slower. Comparisons with Flamsteed's observations of the 
moon showed that such was the case. Newton argued again, 
that as the waters of the ocean are not rigidly attached to the 
earth, they might attract the moon, and be attracted in return, 
independently of the rest of the earth. Certain daily motions 
would then be caused thereby exactly resembling the tides, and 
there were the tides to verify the fact. It was the almost super- 
human power with which he traced out geometrically the conse- 
quences of his theory, and submitted them to repeated compari- 
son with experience, which constitutes his pre-eminence over all 
philosophers. 

3. The Nature of Explanation. 

Explanation is literally the making plain or clear, so 
that there shall be nothing uneven or obscure to inter- 
rupt our view. Scientific explanation consists in har- 
monizing fact with fact, or fact with law, or law with 
law, so that we may see them both to be cases of one 
uniform law of causation. If we hear of a great earth- 
quake in some part of the world, and subsequently hear 
that a neighboring volcano has broken out, we say that 
the earthquake is thus partially explained. The erup- 



COMPLETE METHOD. 255 

tion shows that there were great forces operating be- 
neath the earth's surface, and the earthquake is obvi- 
ously an effect of such causes. The scratches which 
may be plainly seen upon the surface of rocks in cer- 
tain parts of Wales and Cumberland, are explained by 
the former existence of glaciers in those mountains; 
the scratches exactly harmonize with the effects of 
glaciers now existing in Switzerland, Greenland, and 
elsewhere. These may be considered explanations of 
fact by fact. 

A fact may also be explained by a general law of 
nature, that is, the cause and mode of its production 
may be pointed out and shown to "be the same as oper- 
ates in many apparently different cases. Thus the 
cracking of glass by heat may be explained as one result 
of the universal law that heat increases the dimensions 
of solid bodies. The trade-winds are explained as one 
case of the general tendency of warm air to rise and be 
displaced by cold and dense air. The very same simple 
laws of heat and mechanics which cause a draught to flow 
up a chimney when there is a fire below, cause winds 
to blow from each hemisphere towards the equator. 
At the same time the easterly direction from which the 
winds come is explained by the simplest laws of motion ; 
for as the earth rotates from west to east, and moves 
much more rapidly at the equator than nearer the 
poles, the air tends to preserve its slower rate of motion, 
and the earth near the equator moving under it occa- 
sions an apparent motion of the wind from east to 
west. 

There are, according to Mr. Mill, three distinct ways in which 



256 METHOD. 

one law may be explained by other laws, or brought into har- 
mony with them. 

The first is the case where there are really two or more separate 
causes in action, the results of which are combined or added to- 
gether, homogeneously. As was before explained, homogeneous 
intermixture of effects means that the joint effect is simply the 
sum of the separate effects, and is of the same kind with them. 
Our last example of the trade- winds really comes under this case, 
for we find that there is one law or tendency which causes winds 
to blow from the arctic regions towards the equator, and a second 
tendency which causes them to blow from east to west. These 
tendencies are combined together, and cause the trade-winds to 
blow from the north-east in the northern hemisphere, and from 
the south-east in the southern hemisphere. The law according 
to which the temperature of the air is governed in any part of the 
earth is a very complicated one, depending partly on the law by 
which the sun's heating power is governed, partly on the power 
of the earth to radiate the heat away into space, but even more 
perhaps on the effect of currents of air or water in bringing 
warmth or carrying it away. The path of a cannon-ball or other 
projectile is determined by the joint action of several laws ; first, 
the simple law of motion, by which any moving body tends to 
move onward at a uniform rate in a straight line ; secondly, the 
law of gravity, which continually deflects the body towards the 
earth's surface ; thirdly, the resistance of the air, which tends to 
diminish its velocity. 

In the second case of explanation an effect is shown to be due, 
not to the supposed cause directly, but to an intermediate effect 
of that cause. Instead of A being the cause of G, it is found 
that A is the cause of B, and B the cause of G, so that B consti- 
tutes an intermediate link. This explanation may seem to in- 
crease the complexity of the matter, but it really simplifies it ; 
for the connection of A with B may be a case of a familiar and 
simple law, and so may that of B with 0; whereas the law that 
A produces G may be purely empirical and apparently out of har- 
mony with everything else. Thus in lightning it seems as if 
electricity had the power of creating a loud explosion ; but in 
reality electricity only produces heat, and it is the heat which 



COMPLETE METHOD. 257 

occasions sound by suddenly expanding the air. Thus thunder 
comes into harmony with the sound of artillery, which is also 
occasioned by the sudden expansion of the heated gases emitted 
by the powder. When chlorine was discovered it was soon found 
to have a strong power of bleaching, and at the present day 
almost all bleaching is done by chlorine instead of the sun as 
formerly. Inquiry showed, however, that it was not really the 
chlorine which destroyed color, but that oxygen is the inter- 
mediate and active agent. Chlorine decomposes water, and tak- 
ing the hydrogen leaves the oxygen in a state of great activity 
and ready to destroy the organic coloring matter. Thus a num- 
ber of facts are harmonized ; we learn why dry chlorine does not 
bleach, and why there are several other substances which re- 
semble chlorine in its bleaching power, for instance, ozone, 
peroxide of hydrogen, sulphurous acid, and a peculiar oxide of 
vanadium, lately discovered by Dr. Roscoe. It would be impos- 
sible to understand the effect at all unless we knew that it is 
probably due to active oxygen or ozone in all the cases, even in 
the old method of bleaching by exposure to the sun. 

The third and much more important case of explanation is 
where one law is shown to be a case of a more general law. 
As was explained in Section I, we naturally discover the less 
general first, and gradually penetrate to the more simple but pro- 
found secrets of nature. It has often been found that scientific 
men were in possession of several well-known laws without per- 
ceiving the bond which connected them together. Men, for 
instance, had long known that all heavy bodies tended to fall 
towards the earth, and before the time of Newton it was known 
to Hooke, Huyghens, and others, that some force probably con- 
nected the earth with the sun and moon. It was Newton, 
however, who clearly brought these and many other facts under 
one general law, so that each fact or less general law throws 
light upon every other. 

4. Pascal on Method. 

As no treatment of the subject of Method would be 
complete without a reference to Pascal's rules, we here 



258 METHOD. 

add them as prepared by him for the Port Royal 
Logic : 

1. To admit no terms in the least obscure or equivo- 
cal without denning them. 

2. To employ in the definitions only terms perfectly 
known or already explained. 

3. To demand as axioms only truths perfectly evi- 
dent. 

4. To prove all propositions which are at all obscure, 
by employing in their proof only the definitions which 
have preceded, or the axioms which have been accorded, 
or the propositions which have been already demon- 
strated, or the construction of the thing itself which is 
in dispute, when there may be any operation to per- 
form. 

5. Never to abuse the equivocation of terms by fail- 
ing to substitute for them, mentally, the definitions 
which restrict and explain them. 

It may be doubted whether any man ever possessed a more 
acute and perfect intellect than that of Blaise Pascal. He was 
born in 1623, at Clermont in Auvergne, and from his earliest 
years displayed signs of a remarkable character. His father 
attempted at first to prevent his studying geometry, but such was 
Pascal's genius and love of this science, that, by the age of 
twelve, lie had found out many of the propositions of Euclid's 
first book without the aid of any person or treatise. It is difficult 
to say whether he is most to be admired for his mathematical 
discoveries, his invention of the first calculating machine, his 
wonderful Provincial Letters written against the Jesuits, or for 
his profound Pensees or Thoughts, a collection of his reflections 
on scientific and religious topics. 

Among these Thoughts is to be found a remarkable fragment 
upon Logical method, the substance of which is also given in the 



COMPLETE METHOD. 259 

Port Royal Logic. It forms the second article of the Pensees, 
and is entitled Reflexions sur la Geometric en general. As I know- 
no composition in which perfection of truth and clearness of ex- 
pression are more nearly attained, I propose to give in this Section 
a free translation of the more important parts of this fragment, 
appending to it rules of method from the Port Royal Logic, and 
from Descartes' celebrated Essay on Method. The words of Pascal 
are nearly as follows : 

" The true method, which would furnish demonstrations of the 
highest excellence, if it were possible to employ the method 
fully, consists in observing two principal rules. The first rule is 
not to employ any term of which we have not clearly explained 
the meaning ; the second rule is never to put forward any prop- 
osition which we cannot demonstrate by truths already known ; 
that is to say, in a word, to define all the terms, and to prove all 
the propositions. But, in order that I may observe the rules of 
the method which I am explaining, it is necessary that I declare 
what is to be understood by Definition. 

" We recognize in Geometry only those definitions which 
logicians call Nominal Definitions, that is to say, only those 
definitions which impose a name upon things clearly designated 
in terms perfectly known ; and I speak only of those definitions." 

Their value and use is to clear and abbreviate discourse by ex- 
pressing in the single name which we impose what could not 
be otherwise expressed but in several words: provided, neverthe- 
less, that the name imposed remain divested of any other mean- 
ing which it might possess, so as to bear that alone for which we 
intend it to stand. 

" For example, if we need to distinguish among numbers those 
which are divisible into two equal parts, from those which are 
not so divisible, in order to avoid the frequent repetition of this 
distinction, we give a name to it in this manner : — we call every 
number divisible into two equal parts an Even Number. 

" This is a geometrical definition, because after having clearly 
designated a thing, namely any number divisible into two equal 
parts, we give it a name divested of every other meaning which 
it might have, in order to bestow upon it the meaning de- 
signated. 



260 METHOD. 

" Hence it appears that definitions are very free, and that they 
can never be subject to contradiction, for there is nothing more 
allowable, than to give any name we wish to a thing which we 
have clearly pointed out. It is only necessary to take care that 
we do not abuse this liberty of imposing names, by giving the 
same name to two different things. Even that would be allow- 
able, provided that we did not confuse the results, and extend 
them from one to the other. But if we fall into this vice, we 
have a very sure and infallible remedy : it is, to substitute men- 
tally the definition in place of the thing defined, and to hold the 
definition always so present in the mind, that every time we 
speak, for instance, of an even number, we may understand pre- 
cisely that it is a number divisible into two equal parts, and so 
that these two things should be so combined and inseparable in 
thought, that as often as one is expressed in discourse, the mind 
may direct itself immediately to the other. 

"For geometers and all who proceed methodically only impose 
names upon things in order to abbreviate discourse, and not to 
lessen or change the ideas of the things concerning which they 
discourse. They pretend that the mind always supplies the 
entire definition of the brief terms which they employ simply to 
avoid the confusion produced by a multitude of words. 

" Nothing prevents more promptly and effectively the insidious 
fallacies of the sophists than this method, which we should always 
employ, and which alone suffices to banish all sorts of difficulties 
and equivocations. 

" These things being well understood, I return to my explana- 
tion of the true method, which consists, as I said, in defining 
everything and proving everything. 

" Certainly this method would be an excellent one, were it not 
absolutely impossible. It is evident that the first terms we 
wished to define would require previous terms to serve for their 
explanation, and similarly the first propositions we wished to 
prove, would presuppose other propositions preceding them in our 
knowledge ; and thus it is clear that we should never arrive at 
the first terms or first propositions. 

"Accordingly in pushing our researches further and further, we 
arrive necessarily at primitive words which we cannot define, 



COMPLETE METHOD. 261 

and at principles so clear, that we cannot find any principles 
more clear to prove them by. Thus it appears that men are 
naturally and inevitably incapable of treating any science what- 
ever in a perfect method ; but it does not thence follow that we 
ought to abandon every kind of method .... The most perfect 
method available to men consists not in defining everything and 
demonstrating everything, nor in defining nothing and demon- 
strating nothing, but in pursuing the middle course of not 
defining things which are clear and understood by all persons, 
but of defining all others ; and of not proving truths known to 
all persons, but of proving all others. From this method they 
equally* err who undertake to define and prove everything, and 
they who neglect to do it in things which are not self-evident." 

It is made plain in this admirable passage that we can never 
by using words avoid an ultimate appeal to things, because each 
definition of a word must require one or more other words, which 
also will require definition, and so on, ad infinitum. Nor must 
we ever return back upon the words already defined ; for if we 
define A by B, and B by C, and by D, and then B by A, we 
commit what may be called a circulus in definiendo; a most 
serious fallacy, which might lead us to suppose that we know 
the nature of A, B, G, and D, when we really know nothing 
about them. 

5. Descartes on Method. 

We also add here the rules of the celebrated Des- 
cartes for guiding the reason in the attainment of 
truth. They are as follows : 

1. Never to accept anything as true, which we do 
not clearly know to be so ; that is to say, carefully to 
avoid haste or prejudice, and to comprise nothing more 
in our judgments than what presents itself so clearly 
and distinctly to the mind that we cannot have any 
room to doubt it. 

2. To divide each difficulty we examine into as 



262 METHOD. 

many parts as possible, or as may be required for re- 
solving it. 

3. To conduct our thoughts in an orderly manner, 
commencing with the most simple and easily known 
objects, in order to ascend by degrees to the knowledge 
of the most complex. 

4. To make in every case enumerations so complete, 
and reviews so wide, that we may be sure of omitting 
nothing. 

These rules were first stated by Descartes in his admirable 
Discourse on Method, in which he gives his reflections on the 
right mode of conducting the reason, and searching for truth in 
any of the sciences. This little treatise is easily to be obtained 
in the original French, and has also been translated into English 
by Mr. Veitch* The learner can be strongly advised to study 
it. Always to observe the rules of Descartes and Pascal, or to 
know whether we in every case observe them properly, is im- 
possible, but it must nevertheless be valuable to know at what 
we ought to aim. 

Read Locke's brief Essay on the Conduct of the Understanding, 
which contains admirable remarks on the acquirement of 
exact and logical habits of thought ; and Mr. Spencer Baynes' 
Translation of the Port Royal Logic, p. 317 et seq. 

In this Section, on "Complete Method," we have 
considered :— 

1. Empirical and Rational Knowledge. 

2. The Elements of Complete Method. 

3. The Nature of Explanation. 

4. Pascal on Method. 

5. Descartes on Method. 



* Published at Edinburgh in 1850. 



CHAPTER ■¥!!♦ 

RECENT LOGICAL VIEWS. 

The principal part of the preceding chapters is but a 
restatement of what has been taught as constituting the 
science of Logic ever since the days of Aristotle. Some 
additions have, indeed, been made, and they have been 
incorporated with the older doctrines as accepted re- 
sults of thought in this department of knowledge. 
There are, however, certain other views which have not 
been generally adopted as rightly claiming a place in 
the science of Logic, but which, nevertheless, are suffi- 
ciently important to deserve some attention from the 
student of this subject. These new views may be pre- 
sented in outline here in two sections : (1) The 
Quantification of the Predicate; and (2) 
Boole's System of Logic. 



SECTION I. 

THE QUANTIFICATION OF THE PREDICATE. 
1. Meaning of the Expression. 

To quantify the predicate is simply to state whether 
the whole op the part only of the predicate agrees with 
or differs from the subject. In this proposition, 

"All metals are elements," 



264 RECENT LOGICAL VIEWS. 

the subject is quantified, but the predicate is not;' we 
know that all metals are elements, but the proposition 
does not distinctly assert whether metals make the 
whole of the elements or not. In the quantified propo- 
sition 

"All metals are some elements," 

the little word some expresses clearly that in reality 
the metals form only a part of the elements. Aristotle 
avoided the use of any mark of quantity by assuming, 
as we have seen, that all affirmative propositions have 
a particular predicate, like the example just given ; and 
that only negative propositions have a distributed or 
universal predicate. The fact, however, is that he was 
entirely in error, and thus excluded from his system an 
infinite number of affirmative propositions which are 
universal in both terms. It is true that — 

"All equilateral triangles are all equiangular triangles," 

but this proposition could not have appeared in his 
system except in the mutilated form — 

"All equilateral triangles are equiangular." 
Such a proposition as 

"London is the capital of England," 
or "Iron is the cheapest metal," 

had no proper place whatever in his syllogism, since 
both terms are singular and identical with each other, 
and both are accordingly universal. 

2. Conversion with a Quantified Predicate. 

As soon as we allow the quantity of the predicate to 
be stated the forms of reasoning become much simpli- 






QTTANTIFICATIOH OF THE PREDICATE. 265 

fied. We may first consider the process of conversion. 
In our treatment of the subject it was necessary to 
distinguish between conversion by limitation and simple 
conversion. But now one single process of simple con- 
version is sufficient for all kinds of propositions. Thus 
the quantified proposition of the form A, 

"All metals are some elements," 
is simply converted into 

" Some elements are all metals." 
The particular affirmative proposition 

" Some metals are some brittle substances " 
becomes by mere transposition of terms 

" Some brittle substances are some metals." 
The particular negative proposition 

" Some men are not (any) trustworthy persons" 
is also converted into 

"Not any trustworthy persons are some men," 
though the result may appear less satisfactory in this 
form than in the affirmative form, as follows, 

" Some men are some not-trustworthy persons," 
converted simply into 

"Some not-trustworthy persons are some men." 
The universal negative proposition E is converted 
simply as before, and finally we have a new affirmative 
proposition universal both in subject and predicate ; 
as in 

"All equilateral triangles are all equiangular triangles," 
which may obviously be converted simply into 
"'All equiangular triangles are all equilateral triangles." 
12 



266 RECENT LOGICAL VIEWS. 

This doubly universal affirmative proposition is of 
most frequent occurrence ; as in the case of all defi- 
nitions and singular propositions; I may give as in- 
stances "Honesty is the best policy," "The greatest 
truths are the simplest truths/' " Virtue alone is hap- 
piness helow," "Self-exaltation is the fool's paradise." 

3. The Rule for Conversion. 

When affirmative propositions are expressed in the 
quantified form all immediate inferences can be readily 
drawn from them by this one rule, that whatever 
we do with one term tve should do ivith the other 
term. Thus from the doubly universal proposition, 
"Honesty is the best policy," we infer that "what is 
not the best policy is not honesty," and also " what is 
not honesty is not the best policy." From this propo- 
sition in fact we can draw two contra positives ; but the 
learner will carefully remember that from the ordinary 
unquantified proposition A we can only draw one con- 
trapositive (see p. 90). Thus if " metals are elements " 
we must not say that " what are not metals are not 
elements. " But if we quantify the predicate thus, "All 
metals are some elements," we may infer that "what 
are not metals are not some elements." Immediate 
inference by added determinant and complex concep- 
tion can also be applied in either direction to quanti- 
fied propositions without fear of the errors noticed in 
pp. 91, 92. 

4. Number of Propositions with Quantified 
Predicate. 

It is clear that in admitting the mark of quantity 



QUANTIFICATION OF THE PREDICATE. 267 

before the predicate we shall double the number of 
propositions which must be admitted into the syllogism, 
because the predicate of each of the four propositions 
A. E, I, may be either universal or particular. Thus 
we arrive at a list of eight conceivable kinds of propo- 
sitions, which are stated in the following table : 

U All X is all Y. \ 

I Some Xis some Y. ( Affirmative 

A All Xis some Y. ( propositions. 

Y Some X is all Y. ) 

E No Xis (any) Y. ) 

a> Some X is not some Y. I Negative 

n No X is some Y. C propositions. 

Some X is no Y. J 

The letters Xand i^are used to stand for any sub- 
ject and predicate respectively, and the learner by sub- 
stituting various terms can easily make propositions of 
each kind. The symbolic letters on the left-hand side 
were proposed by Archbishop Thomson as a convenient 
mode of referring to each of the eight propositions, 
and are very suitably chosen. The doubly universal 
affirmative proposition is called U ; the simple con- 
verse of A is called Y ; the Greek letter ^ (Eta, e) is 
applied to the proposition obtained by changing the 
universal predicate of E into a particular predicate ; and 
the Greek o> (Omega, 6) is applied to the proposition 
similarly determined from 0. All these eight proposi- 
tions are employed by Sir W. Hamilton, but Archbishop 
Thomson considers that two of them, ^ and o>, are 
never really used. It is remarkable that a complete 
table of the above eight propositions was given by Mr. 
George Bentham in a work called Outline of a New 



268 KECENT LOGICAL VIEWS. 

System of Logic, published in 1827, several years pre- 
vious to the earliest of the logical publications of Sir 
W. Hamilton. But Mr. Bentham considered that some 
of the propositions are hardly to be distinguished from 
others ; as Y from A, of which it is the simple con- 
verse ; or 7i from 0. 

5. Number of Syllogisms with Quantified 
Predicate. 

The employment even of the additional two proposi- 
tions U and Y introduced by Thomson much extends 
the list of possible syllogisms, making them altogether 
62 in number, without counting the fourth figure, 
which is not employed by Hamilton and Thomson. 
When the whole eight propositions are admitted into 
use we are obliged to extend the list of possible syllo- 
gisms so as to contain 12 affirmative and 24 negative 
moods in each of the first three figures. The whole of 
these moods are conveniently stated in the table on 
the next page, given by Archbishop Thomson at p. 188 
of his Laws of TJwught. 

6. Hamilton's Notation. 

Sir W. Hamilton also devised a curious system of 
notation for exhibiting all the moods of the syllogism 
in a clear manner. He always employed the letter M 
to denote the middle term of the syllogism, and the 
two letters and r (the Greek capital letter Gamma) 
for the two terms appearing in the conclusion. 



QUANTIFICATION OF THE PREDICATE. 



269 



Table of Moods of the Syllogism. 





First Figure. 


Second 


Figure. • 


Third Figure. 




Affirm. 


Neg. 


Affirm. 


Neg. 


Affirm. 


Neg. 


i 


uu u 


EUE 
UEE 


UUU 


EUE 
UEE 


UUU 


EUE 
UEE 


11 


AYI 


nYu 
AO o) 


YYI 


OYw 
YOw 


A AI 


7] A CO 

A 7] co 


in 


A AA 


n A r) 


YAA 


A*/ 

Y v n 


AYA 


v Y v 


IV 


YYY 


OYO 
YOO 


AYY 


??YO 
AOO 


TAT 


OAO 
YEO 


V 


All 


7] I CO 

A to to 


YII 


OIco 

Y CO CO 


All 


7) I CO 

A w co 


VI 


IYI 


co Y co 
IOto 


IYI 


to Y co 
IOco 


I AI 


CO A CO 
I 7] CO 


Vll 


UYY 


EYO 

UOO 


UYY 


EYO 
UOO 


UAY 


EAO 

U770 


Vlll 


AU A 


V U rj 

AEt? 


YUA 


YE77 


AU A 


7] U 7] 

A Ev 


IX 


UAA 


EAE 

U v v 


UAA 


EAE 

U v v 


UYA 


EYE 
UO77 


X 


YUY 


ouo 

YEE 


AUY 


77UO 
AEE 


YUY 


OUO 
YEE 


xi 


U II 


EIO 

U 0) (0 


UII 


EIO 

JJ CO CO 


UII 


EIO 

U to to 


xii 


I UI 


CO U CO 

IEt? 


IUI 


to V CO 

IE? 


IUI 


to U to 
IEj; 



The copula of the proposition was indicated by a line thickened 
towards the subject ; thus (7i^""»— if means that " G is 
Jf." To indicate the quantity of the terms Hamilton inserted a 
colon (:) between the term and the copula when the quantity is 
universal, and a comma (,) when the quantity is particular. Thus 
we readily express the following affirmative propositions. 



M All G's are some M'a (A) 
M All G's are all M's (U) 

M Some (7's are some if' s (I) 



and so on. Any affirmative proposition can be converted into 



270 RECENT LOGICAL VIEWS. 

the corresponding negative proposition by drawing a stroke 
through the line denoting the copula, as in the following — 

C : i | : M No C is any M (E) 

G , ■■■ | : M Some G is not any M (0) 

G , ^■■^■t , M Some G is not some M (w) 

Any syllogism can be represented by placing M the middle 
term in the centre and connecting it on each side with the other 
terms. The copula representing the conclusion can then be 
placed below ; Barbara is expressed as follows — 

G , ■■ : M 3 mm : T 

The negative mood Celarent is similarly — 

G : 1 : M , mk : r 

Cesare in the second figure is thus represented — 

G: m ,M: 1 i :r 

I 



7. Hamilton's Canon of the Syllogism. 

Sir W. Hamilton also proposed a new lata or supreme 
canon of the syllogism by which the validity of all 
forms of the syllogism might be tested. This was 
stated in the following words : " What worse relation 
of subject aud predicate subsists between either of two 
terms and a common third term, with which both are 
related, and one at least positively so — that relation 
subsists between these two terms themselves." 

By a worse relation, Sir William means that a negative rela- 
tion is worse than an affirmative, and a particular than a universal. 
This canon thus expresses the rules that if there be a negative 
premise the conclusion must be negative, and if there be a par- 



QUANTIFICATION OF THE PREDICATE. 371 

ticular premise the conclusion must be particular. Special canons 
were also developed for each of the three figures, but in thus 
rendering the system complex the advantages of the quantified 
form of proposition seem to be lost. 

Prof. De Morgan also discovered the advantages of the quanti- 
fied predicate, and invented a system differing greatly from that 
of Sir W. Hamilton. It is fully explained in his Formal Logic, 
The Syllabus of a new System of Logic, and various important 
memoirs on the Syllogism in the Transactions of the Cambridge 
Philosophical Society. In these works is also given a complete 
explanation of the "Numerically Definite Syllogism." Mr. De 
Morgan pointed out that two particular premises may often give 
a valid conclusion provided that the actual quantities of the two 
terms are stated, and when added together exceed the quantity of 
the middle term. Thus if the majority of a public meeting vote 
for the first resolution, and a majority also vote for the second, 
it follows necessarily that some who voted for the first voted also 
for the second. The two majorities added together exceed the 
whole number of the meeting, so that they could not consist of 
entirely different people. They may indeed consist of exactly 
the same people ; but all that we can deduce from the premises 
is that the excess of the two majorities added together over the 
number of the meeting must have voted in favor of each resolu- 
tion. This kind of inference has by Sir W. Hamilton been said 
to depend on ultra-total distribution ; and the name of Plurative 
Propositions has been proposed for all those which give a dis- 
tinct idea of the fraction or number of the subject involved in the 
assertion. 

T. Spencer Baynes, Essay on the new Analytic of Logical 

Forms ; Edinburgh, 1850. 
Prof. Bowen's Treatise on Logic or the Laws of Pure Thought, 

Cambridge, Mass., 1866, gives a full and excellent account of 

Hamilton's Logic. 
See also Hamilton's Lectures on Logic, New York, 1856. 



272 RECENT LOGICAL VIEWS. 

In this Section, on "The Quantification of the 
Predicate," we have considered : 

1. Meaning of the Expression, 

2. Conversion with a Quantified Predicate. 

3. The Rule for Conversion, 

4. Number of Propositions with Quantified Pred- 

icate. 

5. Number of Syllogisms with Quantified Pred- 

icate. 

6. Hamilton's Notation. 

7. Hamilton's Canon of the Syllogism, 



SECTION II. 
BOOLE'S SYSTEM OF LOGIC. 

1. The Difficulty of Dr. Boole's Statement. 

It would not be possible to give in an elementary work 
a notion of the system of indirect inference first dis- 
covered by the late Dr. Boole, the Professor of Mathe- 
matics at the Queen's College, Cork. This system was 
founded upon the Quantification of the Predicate, but 
Dr. Boole regarded Logic as a branch of Mathematics, 
and believed that he could arrive at every possible 
inference by the principles of algebra. The process as 
actually employed by him is very obscure and difficult ; 
and hardly any attempt to introduce it into elementary 
text-books of Logic has yet been made. 

I have been able to arrive at exactly the same results 
as Dr. Boole without the use of any mathematics ; and 
though the very simple process which I am going to 
describe can hardly be said to be strictly Dr. Boole's 



BOOLE'S SYSTEM OF LOGIC. 273 

logic, it is yet very similar to it and can prove every- 
thing that Dr. Boole proved. This Method of Indirect 
Inference is founded upon the three primary Laws of 
Thought, and the learner who may have thought them 
mere useless truisms will perhaps be surprised to find 
how extensive and elegant a system of deduction may 
be derived from them. 

2. Application of the Law of Excluded Middle. 

The Law of Excluded Middle enables us to assert 
that anything must either have a given quality or must 
have it not. Thus if iron be the thing, and combusti- 
bility the quality, any one must see that 

"Iron is either combustible or incombustible." 

This division of alternatives may be repeated as often 
as we like. Thus let booh be the class of things to be 
divided, and English and Scientific two qualities. Then 
any book must be either English or not English ; again 
an English book must be either Scientific or not Scien- 
tific, and the same may be said of books which are not 
English. Thus we *can at once divide books into four 
classes — 

Books, English and Scientific. 
Books, English and not-Scientific. 
Books, not-English and Scientific. 
Books, not-English and not-Scientific. 

This is what we may call an exhaustive division of 
the class boohs ; for there is no possible book which 
does not fall into one division or other of these four, 
for the simple reason, that if it does not fall into any of 
the first three it must fall into the last. The process 



274 RECENT LOGICAL VIEWS. 

can be repeated without end, as long as any new cir- 
cumstance can be suggested as the ground of division. 
Thus we might divide each class again according as the 
books are octavo or not octavo, bound or unbound, 
published in London or elsewhere, and so on. We 
shall call this process of twofold division, which is 
really the process of Dichotomy, the development of a 
term, because it enables us always to develop the utmost 
number of alternatives which need be considered. 

3. Application of the Law of Contradiction. 

As a general rule it is not likely that all the alterna- 
tives thus unfolded or developed can exist, and the next 
point is to ascertain how many do or may exist. The 
Law of Contradiction asserts that nothing can combine 
contradictory attributes or qualities, and if we meet 
with any term which is thus self-contradictory we are 
authorized at once to strike it out of the list. Now 
consider our old example of a syllogism : 

Iron is a metal ; 

All metals are elements ; 

Therefore iron is an element. 

We can readily prove this conclusion by the indirect 
method. For if we develop the term iron, we have four 
alternatives ; thus — 

Iron, metal, element. 

Iron, metal, not-element. 

Iron, not-metal, element. 

Iron, not-metal, not-element. 

But if we compare each of these alternatives with the 
premises of the syllogism, it will be apparent that 



BOOLES' SYSTEM OF LOGIC. 275 

several of them are incapable of existing. Iron, we are 
informed, is a metal. Hence no class of things "iron, 
not-metal " can exist. Thus we are enabled by the first 
premise to strike out both of the last two alternatives 
which combine iron and not-metal. The second alter- 
native, again, combines metal and not-element; but as 
the second premise informs us that "all metals are 
elements," it must be struck out. There remains, then, 
only one alternative which is capable of existing if the 
premises be true, and as there cannot conceivably be 
more alternatives than those considered, it follows dem- 
onstratively that iron occurs only in combination with 
the qualities of metal and element, or, in brief, that it 
is an element. 

4. Universality of the Method. 

We can, however, prove not only the ordinary syllo- 
gistic conclusion, but any other conclusion which can 
be drawn from the same premises ; the syllogistic con- 
clusion is in fact only one out of many which can 
usually be obtained from given premises. Suppose, for 
instance, that we wish to know what is the nature of 
the term or class not-element, so far as we can learn 
it from the premises just considered. We can develop 
the alternatives of this term, just as we did those of 
iron, and get the following — 

Not-element, iron, metal. 
Not-element, iron, not-metal. 
Not-element, not-iron, metal. 
Not-element, not-iron, not-metal. 

Compare these combinations as before with the prem- 



276 RECENT LOGICAL VIEWS. 

ises. The first it is easily seen cannot exist, because 
all metals are elements ; for the same reason the third 
cannot exist ; the second is likewise excluded, because 
iron is a metal and cannot exist in combination with 
the qualities of not-metal. Hence there remains only 
one combination to represent the class desired — namely, 
Not-element, not-iron, not-metal. 
Thus we learn from the premises that every not- 
element is not a metal and is not iron. 

As another example of this kind of deductive process 
I will take a case of the Disjunctive Syllogism, in the 
negative mood, as follows : 

A fungus is either plant or animal, 

A fungus is not an animal ; 

Therefore it is a plant. 

Now if we develop all the possible ways in which 
fungus, plant and animal can be combined together, 
we obtain for the term fungus — 

(1) Fungus, plant, animal. 

(2) Fungus, plant, not-animal. 

(3) Fungus, not-plant, animal. 

(4) Fungus, not-plant, not-animal. 

Of these, however, the 4th cannot exist because by 
the premise a fungus must be a plant, or if not a plant 
an animal. The first and 3d again cannot exist because 
the minor premise informs us that a fungus is not an 
animal. There remains then only the second combi- 
nation, 

Fungus, plant, not-animal, 
from which we learn the syllogistic conclusion that " a 
fungus is a plant." 



boole's system of logic. 277 

5. Comparative Excellence of the System. 

The chief excellence of this mode of deduction con- 
sists in the fact that it is not restricted to any definite 
series of forms like the syllogism, but is applicable, 
without any additional rules, to all kinds of proposi- 
tions or problems which can be conceived and stated. 
There may be any number of premises, and they 
may contain any number of terms ; all we have to do 
to obtain any possible inference is to develop the term 
required into all its alternatives, and then to examine 
how many of these agree with the premises. What 
remain after this examination necessarily form the 
description of the term. The only inconvenience of 
the method is that, as the number of terms increases, 
the number of alternatives to be examined increases 
very rapidly, and it soon becomes tedious to write them 
all out. This work may be abbreviated if we substitute 
single letters to stand for the terms, somewhat as in 
algebra; thus we may take A, B, C, D, etc., to stand 
for the affirmative terms, and a, b, c, d, etc., for the 
corresponding negative ones. 

Let us take as a first example the premises — 
Organic substance is either vegetable or animal. 
Vegetable substance consists mainly of carbon, hydrogen, and 

nitrogen. 
Animal substance consists mainly of carbon, hydrogen, and 
nitrogen. 

It would take a long time to write out all the combinations of 
the four terms occurring in the above ; but if we substitute letters 
as follows — 

A = organic substance, 
B = vegetable substance, 
C = animal substance, 
D = consisting mainly of carbon, hydrogen, and nitrogen, 



AbCD 


(5) 


AbCd 


(6) 


AbcD 


(?) 


Abed 


(8) 



:i78 RECEKT LOGICAL VIEWS. 

we can readily represent all the combinations which can belong 
to the term A. 

(1) ABCD 

(2) ABCd 

(3) ABcD 

(4) ABcd 

Now the premises amount to the statements, that 
A must be either B or 0, 
B must be D, 
C must be D. 

The combinations (7) and (8) are inconsistent with the first 
premise ; the combinations (2) and (4) with the second premise ; 
and (6) is inconsistent with the third premise. There remain 
only, 

ABGD 
ABcD 
AbCD. 

Whence we learn at once that " organic substance (A) always 
consists mainly of carbon, hydrogen and nitrogen," because it 
always occurs in connection with D. The reader may perhaps 
notice that the term AB CD implies that organic substance may 
be both vegetable (B) and animal (C). If the first premise be 
interpreted as meaning that this is not possible, of course this 
combination should also be struck out. It is an unsettled point 
whether the alternatives of a disjunctive proposition can co-exist 
or not (see p. 157), but I much prefer the opinion that they can ; 
and as a matter of fact it is quite likely that there exist very 
simple kinds of living beings, which cannot be distinctly asserted 
to be vegetable only or animal only, but partake of the nature of 
each. 

As a more complicated problem to show the powers of this 
system, let us consider the premises which were treated by Dr. 
Boole in his Laws of Thought, p. 125, as follows : 

" Similar figures consist of all whose corresponding angles are 
equal, and whose corresponding sides are proportional. 

Triangles whose corresponding angles are equal have their 
corresponding sides proportional ; and vice versd. 



boole's system of logic. 279 

Triangles whose corresponding sides are proportional have 
their corresponding angles equal." 

Now if we take oar symbol letters as follows : 
A = similar figure, 
B = triangle, 

C = having corresponding angles equal, 
D= having corresponding sides proportional, 

the premises will he seen to amount to the statements that 

A is identical with GD, 
and that 

BCis identical with BD ; 

in other words, all A's ought to be CD's, CD's ought to he A' a, 
all BG's ought to he BD's and all BD's ought to be BG'a. 

The possible combinations in which the letters may be united 
are 16 in number and are shown in the following table : 



ABGD 


aBGD 


ABCd 


aBCd 


ABcD 


aBcD 


ABcd 


aAcD 


AbGD 


abCD 


AbCd 


abCd 


AbcD 


abeD 


Abed 


abed 



Comparing each of these combinations with the premise, we see 
that ABCd, ABcD, ABcd, and others, are to be struck out be- 
cause every A is also to be CD. The combinations cBCD and 
abCD are struck out because every CD should also be A. Again, 
aBCd is inconsistent with the condition that every BG is also to 
be BD ; and if the learner carefully follows out the same process 
of examination, there will remain only six combinations, which 
agree with all the premises, thus — 

ABGD aBcd 

AbGD abGd 

abeD 
abed 

Prom these combinations we can draw any description we like of 



280 KECENT LOGICAL VIEWS. 

the classes of things agreeing with the premises. The class A or 
similar figures is represented by only two combinations or alter- 
natives ; the negative class a or dissimilar figures, by four com- 
binations, whence we may draw the following conclusion : " Dis- 
similar figures consist of all triangles which have not their 
corresponding angles equal, and sides proportional (aBcd), and of 
all figures, not being triangles, which have either their angles 
equal and sides not proportional (abCd), or their corresponding 
sides proportional and angles not equal (abcD), or neither their 
corresponding angles equal nor corresponding sides proportional 
(abed)." 

6. The Logical Abacus and the Logical Machine. 

In performing this method of inference it is soon 
seen to proceed in a very simple mechanical manner, 
and the only inconvenience is the large number of 
alternatives or combinations to be examined. I have, 
therefore, devised several modes by which the labor can 
be decreased ; the simplest of these consists in engrav- 
ing the series of 16 combinations on the opposite page, 
which occur over and over again in problems, with 
larger and smaller sets, upon a common writing slate, 
so that the excluded ones may be readily struck out 
with a common slate pencil, and yet the series may be 
employed again for any future logical question. A 
second device, which I have called the " Logical aba- 
cus," is constructed by printing the letters upon slips 
of wood furnished with pins, contrived so that any part 
or class of the combinations can be picked out mechani- 
cally with very little trouble ; and a logical problem is 
thus solved by the hand, rather than by the head. 
More recently, however, I have reduced the system to 
a completely mechanical form, and have thus embodied 
the whole of the indirect process of inference in what 



boole's system oe logic. 281 

may be called a Logical Machine. In the front of the 
machine are seen certain movable wooden rods carry- 
ing the set of 16 combinations of letters which are 
seen on page 279. At the foot are 21 keys like 
those of a piano; eight keys towards the left hand 
are marked with the letters A, a, B, b, G, c, D, d, and 
are intended to represent these terms when occurring 
in the subject of a proposition. Eight other keys 
towards the right hand represent the same letters or 
terms when occurring in the predicate. The copula of 
a proposition is represented by a key in the middle of 
the series; the full stop by one to the extreme right, 
while there are two other keys which serve for the dis- 
junctive conjunction or, according as it occurs in sub- 
ject or predicate. Now if the letters be taken to stand 
for the terms of a syllogism or any other logical argu- 
ment, and the keys of the instrument be pressed 
exactly in the order corresponding to the words of the 
premises, the 16 combinations will be so selected and 
arranged thereby that at the end only the possible com- 
binations will remain in view. Any question can then 
be asked of the machine, and an infallible answer will 
be obtained from the combinations remaining. The 
internal construction of the machine is such, therefore, 
as actually to perform the work of inference which, in 
Dr. Boole's system, was performed by a very compli- 
cated mathematical calculation. It should be added, 
that there is one remaining key to the extreme left 
which has the effect of obliterating all previous opera- 
tions and restoring all the combinations to their original 
place, so that the machine is then ready for the per- 
formance of any new problem. 



282 RECENT LOGICAL VIEWS. 

An account of this logical machine may be found in the Pro- 
ceedings of the Royal Society for Jan. 20th, 1870, the machine 
having on that day been exhibited in action to the Fellows of the 
Society. The principles of the method of inference here described 
are more completely stated in The Substitution of Similars* and 
the Pure Logic,\ which I published in the years 1869 and 1864. 
I may add, that the first-named of these works contains certain 
views as to the real nature of the process of inference which I do 
not think it desirable to introduce into an elementary work like 
the present, on account of their speculative character. The pro- 
cess of inference, on the other hand, which I have derived from 
Boole's system, is of so self-evident a character, and is so clearly 
proved to be true by its reduction to a mechanical form, that I do 
not hesitate to bring it to the learner's notice. 

George Boole, Mathematical Analysis of Logic, 1847. 
An Investigation of the Laws of Thought. Londor, Walton & 
Maberly, 1854. 

In this section, on "Boole's System of Logic," 
we have considered :— 

1. The Difficulty of Dr, Boole's Statement, 

2. Application of the Law of Excluded Middle, 

3. Application of the Law of Contradiction, 

4. Universality of the Method 

5. Comparative Excellence of the System. 

6. The Logical Abacus and the Logical Machine, 



* The Substitution of Similars the true Principle of Reasoning, derived from 
a modification of Aristotle 1 s Dictum. Macmillan & Co., 1869. 

t Pure Logic, or the Logic of Quality apart from Quantity, etc. Edward 
Stanford, Charing Cross. 







xercise 



&HG QHEBTIGHS* 



INTRODUCTION. 

1. What is the definition of Logic ? 

2. What are the meanings of a Law of Nature, and a Law of 

Thought ? 

3. Explain the distinction between the Form of Thought, and 

the Matter of Thought. 

4. In what sense may Logic be called the Science of Sciences ? 

5. How does a Science differ from an Art, and why is Logic more 

in the form of a Science than an Art ? 

6. Can we say that Logic is a necessary aid in correct reasoning, 

when persons who have never studied logic reason cor- 
rectly ? 

7. Name the parts of which a syllogism is composed. 

8. How far is it correct to say that Logic is concerned with 

language ? 

9. What are the three acts of mind considered in Logic? Which 

of them is more especially the subject of the Science? 

10. Can you state exactly what is meant by a general notion, 
idea, or conception ? 

11. How do the Nominalists, Realists, and Conceptualists differ 
in their opinions as to the nature of a general notion ? 



284 EXERCISES AND QUESTIONS. 

CHAPTER !♦ 

TERMS. 



SECTION I. 

THE VARIOUS KINDS OF TERMS. 

1. Define a name or term. 

2. What is a categorematic term ? 

3. Explain the distinction between a collective and a general 

term. 

4. Distinguish the collective and distributive use of the word all 

in the following : — 

(1) Non omnis moriar (i. e. I shall not all die). 

(2) "All men find their own in all men's good, 

And all men join in noble brotherhood. " 



(3) Non omnia possumus omnes (i. e. we cannot all do all 

things). 

5. Which of the following are abstract terms ? 

Act, ingratitude, home, hourly, homeliness, introduction, 
individuality, truth, true, trueness, yellow, yellowness, 
childhood, book, blue, intention, reason, rationality, reason- 
ableness. 

6. Define a negative term, and mention the mark by which you 

may recognize it. 

7. Distinguish a privative from a negative term, and find some 

instances of privative terms. 

8. Describe the logical characters of the following terms, with 

the precautions given at p. 28 : 



TEEMS. 



285 



Metropolis 


Consciousness 


Sect 


Book 


Lord Chancellor 


Nation 


Library 


Vegetable Kingdom 


Institution 


Great Britain 


Brilliance 


Light 


Csesar 


Weight 


Observation 


Void 


Sensation 


Tongue 


Gold 


Caesar 


Air 


Prime Minister 


Csesarism 


Mentor 


Indigestibility 


Application 


Anarchy 


Manchester 


Individual 


Retribution 


Recollection 


Volume 


Solemnity 


Insignificant 


Language 


Understanding 


Brilliant 


Adornment 


Geology 


Independence 


Agreement 


Demeanor 


Heaviness 


Obliquity 


Resemblance 


Illustration 


Motionless 


Departure 


Section 


Henry VIII. 


Nestor 


Whiteness 


Formal Logic 


Alexander 



SECTION II. 

THE AMBIGUITY OF TERMS. 

1. Define uni vocal terms, and suggest some terms which are per- 

fectly uni vocal. 

2. What are the "other names by which equivocal terms are often 

called? 

3. Distinguish the three kinds of ambiguous terms, and find 

instances of each. 

4. Distinguish the three causes by which the third and most im- 

portant class of ambiguous terms have been produced. 

5. Explain the ambiguity of any of the following terms, referring 

each to its proper cause, and tracing out as far as possible 
the derivation of each separate meaning from the original 
meaning. 



286 



EXERCISES AND QUESTIONS. 



Bill 


Minister 


Subject 


Letter 


Table 


Clerk 


Object 


Star 


Term 


Order 


Earth 


Pole 


School 


Wood 


Law 


Reason 


Air 


Bull 


Sensation 


Bed 


Glass 


Volume 


Art 


Bowl 


Peer 


Scale 


Interest 


End 


Sense 


Feeling 


Paper 


Division 


Ball 


Kind 


Bolt 


Class 



SECTION III. 



EXTENSION AND INTENSION. 



1. Distinguish very carefully the meanings in extension and in- 

tension of the terms — 
Quadruped, railway, human being, engine, mountain, Mem- 
ber of Parliament. 

2. Enumerate the synonyms or other names used instead of ex- 

tension and intension. 

3. According to what law is the quantity of extension connected 

with the quantity of intension ? Show that the law holds 
true of the following series of terms — 

(1) Iron, metal, element, matter, substance. 

(2) Matter, organized matter, animal, man. 

(3) Ship, steamship, screw-steamship, iron screw- steamship, 

British iron screw-steamship. 

(4) Book, printed book, dictionary, Latin dictionary. 

4. Distinguish between the connotation and denotation of a term. 

5. Select from the list of terms under Section I., Question 8 

(p. 285), such terms as are non-connotative according to Mr. 
Mill's views. 

6. ArraDge the following terms in series as in Question 3, placing 

each term of greater extension before a term of less exten- 
sion. Point out which are the terms of greatest and least 
intension in each series. 



TERMS. 



287 



Emperor 


Animal 


Planet 


Teacher 


Dissenter 


Mammalian 


Baptist 


Individual 


Matter 


Timber 


Jupiter 


Solicitor 


Person 


Ruler 


Quadruped 


Horse 


Organized substance 


Being 


Heavenly body 


Lawyer 


Napoleon III. 


Christian 


Alexander 


Episcopalian 



SECTION IV. 

THE GROWTH OF LANGUAGE 



1. Trace out the generalization or specialization which has taken 

place in any of the following words : 
Kind, genus, class, species, order, rank, Augustus, president, 
speaker, Utopia, rock, Commons, doctor. 

2. Point out metaphors derived from the notions of weight, 

straightness, rock, wind. 

3. Distinguish as accurately as possible the meanings of the fol- 

lowing synonyms : — 

Sickness, malady; mud, mire; confutation, refutation; 
boundary, limit ; mind, intellect ; recollection, reminis- 
cence ; procrastination, dilatoriness ; converse, reverse, 
obverse, inverse. 

4. Form lists of all the words derived from any of the following 

roots : — 

(1) Tendere, to stretch, as in intention, attention. 

(2) Ponere, to place, as in position, supposition. 

(3) Genus, tribe or kind, as in genus, generation. 

(4) Munus, gift, as in remuneration, common (Latin, Com- 

munis). 

(5) Modus, shape or fashion, as in mood, moderate. 

(6) Scribere, to write, as in scribe, inscription, describe. 

(7) Capere to take, as in deception, incipient. 



288 EXEKCISES AND QUESTIONS. 



SECTION V, 

THE PERFECT AND THE IMPERFECT KNOWLEDGE OF 
TERMS. 

1. What are the characters of perfect knowledge ? 

2. Describe the character of the knowledge which we have of the 

following notions or objects : — 
A syllogism. 
Electricity. 
Motion. 
A triangle. 
Eternity. 

The weight of the earth (5852 trillions of tons). 
The color of the sky. 

3. Explain exactly what you mean by intuitive knowledge. 



GHIPTES II, 
PROPOSITIONS. 



SECTION I. 

THE KINDS OF PROPOSITIONS. 
1. Define a proposition, and name the parts of which it is com- 



2. How are propositions classified ? 

3. Name the four kinds of categorical propositions, and their 

symbols. 

4. Under which classes are singular and indefinite propositions 

placed? 

5. Enumerate the most usual signs of the quantity of a proposi- 

tion. 



propositions. 289 

6. What are modal propositions according to early logicians, and 

according to Thomson ? 

7. How far do logicians consider propositions with regard to their 

truth or falsity? 






SECTION II. 

OPPOSITION OF PROPOSITIONS. 

1. State the quantity of the subject and predicate in each of the 

propositions A, E, I, 0. 

2. Select out of the following propositions, pairs of contrary, 

contradictory, subaltern, and subcontrary propositions : — 

(1) Some elements are known. 

(2) No elements are known. 

(3) All elements are known. 

(4) Not all elements are known. 

(5) Some elements are not known. 

(6) All elements are not known. 

3. What propositions are true, false, or doubtful, 

(1) when A is false, (3) when I is false, 

(2) when E is false, (4) when is false ? 

4. Prove by means of the contradictory propositions that subcon- 

trary propositions cannot both be false. 

5. Show by means of the subcontrary propositions that contrary 

propositions may both be false. 

6. What quantity would you assign to each of the following 

propositions ? 

(1) Knowledge is power. 

(2) Nebulge are material bodies. 

(3) Light is the vibration of an ether. 

(4) Men are more to be trusted than we think. 

(5) The Chinese are industrious. 

7. Why is it desirable in controversy to refute a statement by its 

contradictory and not by its contrary ? 

13 



290 EXERCISES AND QUESTIONS. 

SECTION III. 

CONVERSION AND IMMEDIATE INFERENCE. 

1. Define inference and conversion. 

2. What are converse and convertend propositions ? 

3. State the rules of valid conversion. 

4. Name all the kinds of conversion. 

5. By what process do we pass from each of the following prop- 

ositions to the next ? 

(1) No knowledge is useless. 

(2) No useless thing is knowledge. 

(3) All knowledge is not useless. 

(4) All knowledge is useful. 

(5) What is not useful is not knowledge. 

(6) What is useless is not knowledge. 

(7) No knowledge is useless. 

6. Give the logical opposites of the following proposition, and 

the converse of its contradictory : 

" He cannot become rich who will not labor." 

7. Apply negative conception to the proposition "All men are 

fallible ; " then convert and show that the result is the con- 
trapositive of the original. 

8. Classify the propositions subjoined into the four following 

groups : 

a. Those which can be inferred from (1). 

b. Those from which (1) can be inferred. 

c. Those which do not contradict (1), but cannot be inferred 

from it. 

d. Those which contradict (1). 

(1) All just acts are expedient acts. 

(2) No expedient acts are unjust. 

(3) No just acts are inexpedient. 

(4) All inexpedient acts are unjust. 

(5) Some unjust acts are inexpedient. 

(6) No expedient acts are just. 

(7) Some inexpedient acts are unjust. 



PROPOSITIONS. 291 



(8) All expedient acts are just. 

(9) No inexpedient acts are just. 

(10) All unjust acts are inexpedient. 

(11) Some inexpedient acts are just acts. 

(12) Some expedient acts are just. 

(13) Some just acts are expedient. 

(14) Some unjust acts are expedient. 



SECTION IV. 

THE LOGICAL ANALYSIS OF SENTENCES. 

1. How does the grammatical predicate differ from the logical 

predicate ? 

2. Distinguish between a compound and a complex sentence ; and 

between co-ordinate and subordinate propositions. 

3. Enumerate the grammatical expressions which may form 

(1) A subject. (4) An object. 

(2) An attribute. (5) An adverbial. 

(3) A predicate. 

4. Examine the following sentences, ascertain which are com- 

pound or complex, and point out the co-ordinate or subordi- 
nate propositions: 

(1) Happy is the man that findeth wisdom, and the man that 

getteth understanding. 

(2) Heat, being motion, can be converted into mechanical 

force. 

(3) Ceres, Pallas, Juno, and Vesta are minor planets, or 

asteroids. 

(4) Knowledge comes, but wisdom lingers. 

(5) Fortune often sells to the hasty what she gives to those 

who wait. 

(6) Thousands at His bidding speed, 
And post o'er land and ocean without rest ; 
They also serve who only stand and wait. 

(7) Pride that dines on vanity, sups on contempt. 



292 EXERCISES AND QUESTIONS. 

(8) Nobody can be healthful without exercise, neither natural 

body, nor politic. 

(9) Nature is often hidden, sometimes overcome, seldom ex- 

tinguished. 

(10) It is impossible to love and be wise. . 

(11) Though gods they were, as men they died. 

(12) He that is not industrious envieth him that is. 

(13) Ye are my friends, if ye do whatsoever I command you. — 

John xv. 14. 

(14) The wisdom that is from above is first pure, then peace- 

able, gentle, and easy to be intreated, full of mercy, and 
good fruits, without partiality, and without hypocrisy. — 
James iii. 17. 
5. Analyze in the form of a scheme or diagram any of the follow- 
ing sentences : — 

(1) The first aphorism of Bacon's Novum Organum, on p. 202. 

(2) Some judgments are merely explanatory of their subject, 

having for their predicate, a conception which it fairly 
implies, to all who know and can define its nature. 

(3) There be none of the affections which have been noted to 

fascinate or bewitch, but love and envy ; they both have 
vehement wishes ; they frame themselves readily into 
imaginations and suggestions ; and they come easily into 
the eye, especially upon the presence of the objects, which 
are the points that conduce to fascination, if any such 
there be. 

GENERAL EXERCISES ON PROPOSITIONS. 

The learner is desired to ascertain the logical character of each 
of the following propositions ; he is to state of each whether it is 
affirmative or negative, universal, particular, singular or in- 
definite, pure or modal, exclusive or exceptive, etc. ; when 
irregularly stated he is to reduce the proposition to the simple 
logical order ; he is then to convert the proposition, and to draw 
immediate inferences from it by any process which may be 
applicable. 

(1) All birds are feathered. 

(2) No reptiles are feathered. 



PROPOSITIONS. 293 

(3) Fixed stars are self-luminous. 

(4) Perfect happiness is impossible. 

(5) Life every man holds dear. 

(6) Every mistake is not a proof of ignorance. 

(7) Some of the most valuable books are seldom read. 

(8) He jests at scars who never felt a wound. 

(9) Heated metals are softened. 

(10) Not one of the Greeks at Thermopylae escaped. 

(11) Few are acquainted with themselves. 

(12) Whoso loveth instruction loveth knowledge. 

(13) Nothing is harmless that is mistaken for a virtue. 

(14) Some of our muscles act without volition. 

(15) Metals are all good conductors of heat. 

(16) Fame is no plant that grows on mortal soil. 

(17) Only the brave deserve the fair. 

(18) No one is free who doth not command himself. 

(19) Nothing is beautiful except truth. 

(20) The wicked shall fall by his own wickedness. 

(21) Unsafe are all things unbecoming. 

(22) There is no excellent beauty that hath not some strange- 

ness in the proportion. 

(23) It is a poor centre of a man's actions, himself. 

(24) Mercy but murders, pardoning those that kill. 

(25) I shall not all die. (Non omnis moriar.) 

(26) A regiment consists of two battalions. 

(27) 'Tis cruelty to load a falling man. 

(28) Every mistake is not culpable. 

(29) Quadrupeds are vertebrate animals. 

(30) Not many of the metals are brittle. 

(31) Many are the deserving men who are unfortunate. 

(32) Amalgams are alloys of mercury. 

(33) One kind of metal at least is liquid. 

(34) Talents are often misused. 

(35) Some parallelograms have their adjoining sides equal. 

(36) Britain is an island. 

(37) Romulus and Remus were twins. 

(38) A man's a man. 

(39) Heaven is all mercy. 



294 EXERCISES AlsTD QUESTIONS. 

(40) Every one is a goo J judge of his own interests. 

(41) All parallelograms have their opposite angles equal. 

(42) Familiarity breeds contempt. 

(43) No one is always happy. 

(44) Every little makes a mickle. 



CHAPTER III. 
SYLLOGISMS. 

SECTION I. 
THE LAWS OF THOUGHT. 

1. State the three Fundamental Laws of Thought, and apply them 

to the following notions : 

(1) Matter, organic, inorganic. 

(2) Undulations, polarized, non-polarized. 

(3) Figure, rectilinear, curvilinear. 

2. Is it wrong to assert that an animal cannot both be vertebrate 

and invertebrate, seeing that some animals are vertebrate 
and some are not ? 

3. Select from the following such terms as are negatives of the 

others, and such as are opposites : — Light, plenum, gain, 
heat, decrease, loss, darkness, cold, increase, vacuum. 

4. How is Aristotle's dictum applicable to the following argu- 

ments? 

(1) Silver is a good conductor of electricity ; for such are all 

the metals. 

(2) Comets cannot be without weight ; for they are composed 

of matter, which is not without weight. 



SYLLOGISMS. 295 

SECTION II. 

THE RULES OF THE SYLLOGISM. 

1. Distinguish mediate and immediate inference. 

2. Define syllogism, and state with what it is synonymous. 

3. What are the six principal and two subordinate rules of the 

syllogism ? 

4. In the following syllogisms point out in succession the con- 

clusion, the middle term, the major term, the minor term, 
the major premise and the minor premise, observing this 
precise order. 

(1) All men are fallible ; 
All kings are men ; 

Therefore all kings are fallible. 

(2) Platinum is a metal ; 

All metals combine with oxygen ; 
Therefore Platinum combines with oxygen. 
(3) Hottentots are capable of education ; for Hottentots are 
men, and all men are capable of education. 

5. Explain carefully what is meant by non-distribution of the 

middle term. 



SECTION III. 

THE MOODS AND FIGURES OF THE SYLLOGISM. 

1. Name the rules of the syllogism which are broken by any of 

the following moods, no regard being paid to figure : — 
AIA, EEI, IE A, IOI, HA, AEI, 

2. Write out all the 64 moods of the syllogism and strike out the 

53 invalid ones. 

3. Show in what figures the following premises give a valid con- 

clusion : — AA, AI, EA, OA. 

4. In what figures are I E O and EI valid ? 



296 EXERCISES AND QUESTIONS. 

5. To what moods do the following valid syllogisms belong? 

Arrange them in correct logical order. 
(1) Some Y's are Z's. (2) All Z's are Y's. 

No X's are Y's. No Y's are X's. 

Some Z's are not X's. No Z's are X's. 

(3) No fish suckles its young ; 

The whale suckles its young ; 

Therefore the whale is no fish. 

6. Deduce conclusions from the following premises ; and state to 

what mood the syllogism belongs. 

(1) Some amphibious animals are mammalian. 
All mammalian animals are vertebrate. 

(2) All planets are heavenly bodies. 
No planets are self-luminous. 

(3) Mammalian animals are quadrupeds. 
No birds are quadrupeds. 

(4) Ruminant animals are not predaceous. 
The lion is predaceous. 

7. Invent examples to show that false premises may give true 

conclusions. 

8. Supply premises to the following conclusions . 

(1) Some logicians are not good reasoners. 

(2) The rings of Saturn are material bodies. 

(3) Party government exists in every democracy. 

(4) All fixed stars obey the law of gravitation. 



SECTION IV. 

THE REDUCTION OF SYLLOGISMS. 

1. State and explain the mnemonic lines Barbara, Celarent, etc, 

2. Construct syllogisms in each of the following moods, taking 

X, Y, Z, for the major, middle, and minor terms respectively, 

and show how to reduce them to the first figure : 

Cesare, Festino, Darapti, Datisi, Ferison, Camenes, Fesapo. 

3. What is the use of Reduction ? 

4. Prove that the following premises cannot give a universal 

conclusion— EI, IA, OA, IE. 



SYLLOGISMS. 297 

5. Prove that the third figure must have an affirmative minor 

premise, and a particular conclusion. 

6. Reduce the moods Cesare and Camenes by the Indirect method, 

or Reductio ad Impossibile. 



SECTION V. 
IRREGULAR AND COMPOUND SYLLOGISMS. 

1. Describe the meaning of each of the terms — Enthymeme, 

Prosyllogism, Episyllogism, Epicheirema, Sorites. 

2. Make an example of a syllogism in which there are two pro- 

syllogisms. 

3. Construct a sorites of four premises and resolve it into distinct 

syllogisms. 

4. What are the rules to which a sorites must conform ? 

5. The learner is requested to analyze the following arguments, 

to detect those which are false, and to ascertain the rules of 
the syllogism which they break ; if the argument appears 
valid he is to ascertain the figure and mood to which it 
belongs, to state it in correct logical form, and then if it be 
in an imperfect figure to prove it by reduction to the first 
figure. The first six of the examples should be arranged 
both in the extensive and intensive orders. 

(1) None but mortals are men. 
Monarchs are men. 
Therefore monarchs are mortals. 

(2) Personal deformity is an affliction of nature. 
Disgrace is not an affliction of nature. 
Therefore personal deformity is not disgrace. 

(3) Some statesmen are also authors ; for such are Mr. Glad- 

stone, Lord Derby, Lord Russell, and Sir G. C. Lewis. 

(4) This explosion must have been occasioned by gunpowder ; 

for nothing else would have possessed sufficient force. 

(5) Every man should be moderate ; for excess will cause dis- 



{G) Blessed are the merciful ; for they shall obtain mercy. 



298 EXERCISES AND QUESTIONS. 

(7) As almost all the organs of the body have a known use, 

the spleen must have some use. 

(8) Cogito, ergo sum. (I think, therefore I exist.) 

(9) Some speculative men are unworthy of trust ; for they are 

unwise, and no unwise man can be trusted. 

(10) No idle person can be a successful writer of history; 

therefore Hume, Macaulay, Hallam and Grote must have 
been industrious. 

(11) Who spareth the rod, hateth his child ; the parent who 

loveth his child therefore spareth not the rod. 

(12) Comets must consist of heavy matter ; for otherwise they 

would not obey the law of gravitation. 

(13) Lithium is an element ; for it is an alkali-producing sub- 

stance, which is a metal, which is an element. 

(14) Rational beings are accountable for their actions ; brutes 

not being rational, are therefore exempt from responsi- 
bility. 

(15) A singular proposition is a universal one ; for it applies to 

the whole of its subject. 

(16) Whatever tends to withdraw the mind from pursuits of 

a low nature deserves to be promoted ; classical learning 
does this, since it gives us a taste for intellectual enjoy- 
ments ; therefore it deserves to be promoted. 

(17) Bacon was a great lawyer and statesman ; and as he was 

also a philosopher, we may infer that any philosopher may 
be a great lawyer and statesman. 

(18) Immoral companions should be avoided ; but some im- 

moral companions are intelligent persons, so that some 
» intelligent persons should be avoided. 

(19) Mathematical study undoubtedly improves the reasoning 

powers ; but, as the study of logic is not mathematical 
study, we may infer that it does not improve the reasoning 
powers. 

(20) Every candid man acknowledges merit in a rival ; every 

learned man does not do so ; therefore every learned man 
is not candid. 



SYLLOGISMS. 299 



SECTION VI. 

CONDITIONAL ARGUMENTS. 

1. What are the kinds of conditional propositions, and by what 

signs can you recognize them ? 

2. What are the rules of the hypothetical syllogism? 

3. To what categorical fallacies do breaches of these rules cor- 

respond ? 

4. Select from the following such as are valid arguments, and 

reduce them to the categorical form ; explain the fallacious 
reasoning in the others : 

(1) Rain has fallen if the ground is wet; but the ground is 

not wet ; therefore rain has not fallen. 

(2) If rain has fallen, the ground is wet ; but rain has not 

fallen ; therefore the ground is not wet. 

(3) The ground is wet, if rain has fallen ; the ground is wet ; 

therefore rain has fallen. 

(4) If the ground is wet, rain has fallen ; but rain has fallen ; 

therefore the ground is wet. 
N. B. — In these as in other logical examples the student must 
argue only from the premises, and not from any other knowledge 
of the subject-matter. 

5. Show that the canons of syllogism (pp. 108, 109) may be 

stated indifferently in the hypothetical or categorical form. 

6. State the following in the form of a Disjunctive or Dilemmatic 

argument, and name the kind to which it belongs. 
If pain is severe it will be brief; and if it last long it will be 
slight ; therefore it is to be patiently borne. 



300 EXERCISES AND QUESTION'S. 



CHAPTER IY, 

FALLACIES. 

1. Classify fallacies. 

2. Explain the following expressions : 

Adicto secundum quid ad dictum simpliciter; ignoratio elenchi ; 
argumentum ad hominem ; argumentum ad populum ; 
petitio principii ; circulus in probando ; non sequitur ; post 
hoc ergo propter hoc. 

3. What is arguing in a circle ; and what is a question-begging 

epithet ? » 

4. What differences of meaning may be produced in the follow- 

ing sentence by varying the accent ? 
"Newton's discovery of gravitation is not generally believed 
to have been at all anticipated by several philosophers in 
England and Holland." 

5. Point out the misinterpretations to which the following sen- 

tences might be liable. 

(1) He went to London and then to Brighton by the express 

train. 

(2) Did you make a long speech at the meeting ? 

(3) How much is five times seven and nine ? 

6. The following examples consist partly of true and partly of 

false arguments. The learner is requested to treat them as 
follows : 

(1) If the example is not in a simple and complete logical form, 

to complete it in the form which appears most appropriate. 

(2) To ascertain whether it is a valid or fallacious argument. 

(3) To assign the exact name of the argument or fallacy as the 

case may be. 

(4) If a categorical syllogism, to reduce it to the first figure. 

(5) If a hypothetical syllogism, to state it in the categorical 

form. 



FALLACIES. 301 



EXAMPLES OF ARGUMENTS. 



1. Elementary substances alone are metals. Iron is a metal; 

therefore it is an elementary substance. 

2. No Athenians could have been Helots ; for all the Helots were 

slaves, and all Athenians were free men. 

3. Aristotle must have been a man of extraordinary industry ; 

for only such a man could have produced his works. 

4. Nothing is better than wisdom ; dry bread is better than 

nothing ; therefore dry bread is better than wisdom. 

5. Pitt was not a great and useful minister ; for though he would 

have been so had he carried out Adam Smith's doctrines of 
Free Trade, he did not carry out those doctrines. 

6. Only the virtuous are truly noble ; some who are called noble 

are not virtuous ; therefore some who are called noble are 
not truly noble. 

7. Ireland is idle and therefore starves ; she starves, and there- 

fore rebels. 

8. No designing person ought to be trusted ; engravers are by 

profession designers ; therefore they ought not to be trusted. 

9. Logic as it was cultivated by the schoolmen proved a fruitless 

study ; therefore Logic as it is cultivated at the present day 
must be a fruitless study likewise. 

10. Is a stone a body ? Yes. Then is not an animal a body ? 
Yes. Are you an animal ? I think so. Ergo, you are a 
stone, being a body. — Lucian. 

11. If ye were Abraham's children, ye would do the works of 

Abraham. — John viii. 39. 

12. He that is of God heareth God's words : ye therefore hear 
them not, because ye are not of God. — John viii. 47. 

13. Mahomet was a wise lawgiver ; for he studied the character 
of his people. 

14. Every one desires virtue, because every one desires happi- 



15. His imbecility of character might have been inferred from 
his proneness to favorites ; for all weak princes have this 
failing. — Be Morgan. 

16. He is brave who conquers his passions ; he who resists temp- 



302 EXERCISES AND QUESTIONS. 

tation conquers his passions ; so that he who resists temp- 
tation is brave. 

17. Suicide is not always to be condemned ; for it is but volun- 

tary death, and this has been gladly embraced by many of 
the greatest heroes of antiquity. 

18. Since all metals are elements, the most rare of all the metals 

must be the most rare of all the elements. 

19. The express train alone does not stop at this station ; and as 

the last train did not stop it must have been the express 
train. 

20. Peel's remission of taxes was beneficial ; the taxes remitted 

by Peel were indirect ; therefore the remission of indirect 
taxes is beneficial. 

21. Books are a source both of instruction and amusement ; a 

table of logarithms is a book ; therefore it is a source both of 
instruction and amusement. 

22. All desires are not blameable ; all desires are liable to ex- 

cess ; therefore somethings liable to excess are not blameable. 

23. Whosoever intentionally kills another should suffer death ; a 

soldier, therefore, who kills his enemy should suffer death. 

24. Projectors are unfit to be trusted ; this man has formed a 

project ; therefore he is unfit to be trusted. 

25. Few towns in the United Kingdom have more than 300,000 

inhabitants ; and as all such towns ought to be represented 
by three members in Parliament, it is evident that few 
towns ought to have three representatives. 
2G. All the works of Shakspeare cannot be read in a day ; there- 
fore the play of Hamlet, being one of the works of Shak- 
speare, cannot be read in a day. 

27. In moral matters we cannot stand still ; therefore he who 

does not go forward is sure to fall behind. 

28. The people of the country are suffering from famine ; and as 

you are one of the people of the country you must be suffer- 
ing from famine. 

29. Those substances which are lighter than water can float upon 

it ; those metals which can float upon it are potassium, 
sodium, lithium, etc.; therefore potassium, sodium, lithium, 
etc., are lighter than water. 






FALLACIES. 303 

30. The laws of nature must be ascertained by Deduction, Tra- 

duction or Induction ; but the former two are insufficient for 
the purpose ; therefore the laws of nature must be ascertained 
by Induction. 

31. A successful author must be either very industrious or very 

talented ; Gibbon was very industrious, therefore he was 
not very talented. 

32. You are not what I am ; I am a man ; therefore you are not a 

man. 

33. The holder of some shares in a lottery is sure to gain a 

prize ; and as I am the holder of some shares in a lottery I 
am sure to gain a prize. 

34. Gold and silver are wealth ; and therefore the diminution of 

the gold and silver in the country by exportation is the 
diminution of the wealth of the country. 

35. Over-credulous persons ought never to be believed ; and as 

the Ancient Historians were in many instances over-credu- 
lous they ought never to be believed. 

36. Some mineral compounds are not decomposed by heat ; all 

organic substances are decomposed by heat; therefore no 
organic substances are mineral compounds. 

37. Whatever schools exclude religion are irreligious ; Non- 

sectarian schools do not allow the teaching of religious 
creeds ; therefore they are irreligious. 

38. Night must be the cause of day ; for it invariably precedes it. 

39. The ancient Greeks produced the greatest master-pieces of 

eloquence and philosophy ; the Lacedaemonians were ancient 
Greeks ; therefore they produced the greatest master- pieces 
of eloquence and philosophy. 

40. All presuming men are contemptible ; this man, therefore, is 

contemptible ; for he presumes to believe his opinions are 
correct. 

41. If a substance is solid it possesses elasticity, and so also it does 

if it be liquid or gaseous ; but all substances are either solid, 
liquid or gaseous ; therefore all substances possess elasticity. 

42. If Parr's life pills are of any value those who take them will 

improve in health ; now my friend who has been taking 
them has improved in health ; therefore they are of value. 



304 EXEKCISES AtfD (QUESTIONS. 

43. He who calls you a man speaks truly ; he who calls you a 

fool calls you a man ; therefore he who calls you a fool 
speaks truly. 

44. Who is most hungry eats most; who eats least is most 

hungry ; therefore who eats least eats most. 

45. What produces intoxication should be prohibited ; the use of 

spirituous liquors causes intoxication ; therefore the use of 
spirituous liquors should be prohibited. 

46. What we eat grew in the fields ; loaves of bread are what we 

eat ; therefore loaves of bread grew in the fields. 

47. If light consisted of material particles it would possess mo- 

mentum ; it cannot therefore consist of material particles, 
for it does not possess momentum. 

48. Everything is allowed by law which is morally right ; in- 

dulgence in pleasures is allowed by law ; therefore indul- 
gence in pleasures is morally right. 

49. All the trees in the park make a thick shade ; this is one of 

them, therefore this tree makes a thick shade. 

50. All visible bodies shine by their own or by reflected light. 

The moon does not shine by its own, therefore it shines by 
reflected light ; but the sun shines by its own light, there- 
fore it cannot shine by reflected light. 

51. Honesty deserves reward ; and a negro is a fellow-creature ; 

therefore, an honest negro is a fellow-creature deserving of 
reward. 

52. Nearly all the satellites revolve round their planets from 

west to east ; the moon is a satellite ; therefore it revolves 
round its planet from west to east. 

53. Italy is a Catholic country and abounds in beggars ; France 

is also a Catholic country, and therefore abounds in beg- 
garsi 

54. Every law is either useless or it occasions hurt to some per- 

son ; now a law that is useless ought to be abolished ; and 
so ought every law that occasions hurt ; therefore every 
law ought to be abolished. 

55. The end of a thing is its perfection ; death is the end of life ; 

therefore death is the perfection of life. 

56. When we hear that all the righteous people are happy, it is 



FALLACIES. 305 

hard to avoid exclaiming, What ! are all the unhappy per- 
sons we see to be thought unrighteous ? 

57. I am offered a sum of money to assist this person in gaining 

the office he desires ; to assist a person is to do him good, 
and no rule of morality forbids the doing of good ; therefore 
no rule of morality forbids me to receive the sum of money 
for assisting the person. 

58. Ruminant animals are those which have cloven feet, and 

they usually have horns ; the extinct animal which left this 
foot-print had a cloven foot ; therefore it was a ruminant 
animal and had horns. Again, as no beasts of prey are 
ruminant animals it cannot have been a beast of prey. 

59. We must either gratify oar vicious propensities, or resist 

them ; the former course will involve us in sin and misery ; 
the latter requires Self-denial; therefore we must either fall 
into sin and misery or practise self-denial. 

60. The stonemasons are benefited by the masons' union ; the 

bricklayers by the bricklayers' union ; the hatmakers by the 
hatmakers' union ; in short, every trade by its own union ; 
therefore it is evident that if all workmen had unions all 
workmen would be benefited thereby. 

61. Every moral aim requires the rational means of attaining it ; 

these means are the establishment of laws ; and as happiness 
is the moral aim of man it follows that the attainment of 
happiness requires the establishment of laws. 

62. He that can swim needs not despair to fly ; for to swim is to 

fly in a grosser fluid, and to fly is to swim in a subtler. 

63. The Helvetii, if they went through the country of the 

Sequani, were sure to meet with various difficulties ; and if 
they went through the Roman province, they were exposed 
to the danger of opposition from Caesar ; but they were 
obliged to go one way or the other ; therefore they were 
either sure of meeting with various difficulties, or of being 
exposed to the danger of opposition from Caesar. — De Bello 
Gallico, lib. i. 6. 

64. Riches are for spending, and spending for honor and good 

actions; therefore extraordinary expense must be limited 
by the worth of the occasion. — Bacon. 



306 EXERCISES AND QUESTIONS. 

65. If light is not refracted near the surface of the moon, there 

cannot be any twilight ; but if the moon has no atmosphere 
light is not refracted near its surface ; therefore.if the moon 
has no atmosphere there cannot be any twilight. 

66. The preservation of society requires exchange ; whatever re- 

quires exchange requires equitable valuation of property ; 
this requires the adoption of a common measure ; hence the 
preservation of society requires the adoption of a common 
measure. 

67. The several species of brutes being created to prey upon one 

another proves that the human species were intended to 
prey upon them. 

68. The more correct the logic, the more certainly the conclusion 

will be wrong if the premises are false. Therefore where 
the premises are wholly uncertain, the best logician is the 
least safe guide. 

69. If our rulers could be trusted always to look to the best 

interests of their subjects, monarchy would be the best form 
of government ; but they cannot be trusted ; therefore 
monarchy is not the best form of government. 

70. If men were prudent, they would act morally for their own 

good ; if benevolent, for the good of others. But many men 
will not act morally, either for their own good, or that of 
others ; such men, therefore, are not prudent or benevolent. 

71. He who bears arms at the command of the magistrate does 

what is lawful for a Christian ; the Swiss in the French ser- 
vice, and the British in the American service, bore arms af 
the command of the magistrate ; therefore they did what 
was lawful for a Christian. — Whately. 

72. A man that hath no virtue in himself ever envieth virtue in 

others ; for men's minds will either feed upon their own 
good or upon others' evil ; and who wanteth the one will 
prey upon the other. — Bacon. 

73. The object of war is durable peace ; therefore soldiers are the 

best peace-makers. 

74. Confidence in promises is essential to the intercourse of 

human life ; for without it the greatest part of our conduct 
would proceed upon chance. But there could be no confi- 



FALLACIES. 307 

dence in promises, if men were not obliged to perform them ; 
the obligation, therefore, to perform promises is essentia] to 
the same ends and in the same degree. 

75. If the majority of those who use public-houses are prepared 

to close them, legislation is unnecessary ; but if they are not 
prepared for such a measure, then to force it on them by out- 
side pressure is both dangerous and unjust. 

76. He who believes himself to be always in the right in his 

opinion, lays claim to infallibility ; you always believe your- 
self to be in the right in your opinion ; therefore you lay 
claim to infallibility. — Whately. 

77. If we never find skins except as the teguments of animals, we 

may safely conclude that animals cannot exist without skins. 
If color cannot exist by itself, it follows that neither can any- 
thing that is colored exist without color. So, if language 
without thought is unreal, thought without language must 
also be so. 

78. No soldiers should be brought into the field who are not well 

qualified to perform their part ; none but veterans are well 
qualified to perform their part ; therefore none but veterans 
should be brought into the field. — Whately. 

79. The minimum visibile is the least magnitude which can be 

seen ; no part of it alone is visible, and yet all parts of it 
must affect the mind in order that it may be visible ; there- 
fore, every part of it must affect the mind without being 
visible. 

80. The scarlet poppy belongs to the genus Papaver, of the 

natural order Papaveraceae ; which again is part of the sub- 
class Thalamiflorae, belonging to the great class of Dicotyle- 
dons. Hence the scarlet poppy is one of the Dicotyledons. 

81. Improbable events happen almost every day; but what 

happens almost every day is a very probable event ; there- 
fore improbable events are very probable events. — Whately. 



308 EXERCISES AtfD QUESTIONS. 

CHAPTER Y. 

INDUCTION. 



SECTION I. 

THE INDUCTIVE SYLLOGISM. 



1. How do Induction and Deduction differ? 

2. Find an instance of reasoning in Traduction. 

3. Distinguish Perfect and Imperfect Induction. 

4. How does Mr. Mill define Induction, and what is his opinion 

of Imperfect Induction ? 

5. What is the use of Perfect Induction ? 

6. Construct some instances of the inductive syllogism, and 

show that they may be thrown into a disjunctive form. 



SECTION II. 
THE FORMS OF INDUCTION. 

1. From what circumstance arise the certainty and generality of 

reasoning in geometry ? 

2. Find other instances of certain and general reasoning concern- 

ing the properties of numbers. 

3. Why are inductive conclusions concerning prime numbers un- 

certain and not general ? 

4. Why is a single instance sometimes sufficient to warrant a 

universal conclusion, while in other cases the greatest pos- 
sible number of concurring instances, without any exception, 
is not sufficient to warrant such a conclusion ? 

5. What are the strict and ordinary meanings of the word 

analogy ? 



METHOD. 309 



CHAPTER YI* 

METHOD. 

SECTION I. 

INDUCTIVE METHOD. 

1. What is the false method of Science against which Bacon pro- 

tested ? 

2. Explain the exact meaning of Bacon's assertions, that man is 

the Servant and Interpreter of Nature, and that Knowledge 
is Power. 

3. How does experiment differ from observation ? 

4. Classify the sciences according as they employ passive obser- 

vation, experiment, or both. 

5. Name the chief points in which experiment is superior to 

mere observation. 

6. What is the principal precaution needful in observation ? 

7. Explain how it is possible to anticipate nature and yet 

establish all conclusions upon the results of experience. 

8. Define exactly what is meant by a cause of an event, and 

distinguish cause, occasion, antecedent. 

9. Point out all the causes concerned in the following phe- 

nomena : 

(1) The burning of a fire. 

(2) The ordinary growth of vegetables. 

(3) The cracking of a glass by hot water. 

10. State and explain in your own words Mr. Mill's first three 

Canons of Inductive Method. 

11. Point out exactly how the Joint Method differs from the 

simple Method of Difference. 

12. Give some instances of simple experiments fulfilling com- 

pletely the conditions of the Method of Difference. 



:>10 EXERCISES AKD QUESTIONS. 

13. What can you infer from the following instances? 
Antecedents. Consequents. 

ABBE stqp 

BOB qsr 

BFG vqu 

ABB. tsp 

EK. xquo 

ABFG pquv 

ABE. pqt. 



SECTION II. 

DEDUCTIVE METHOD. 



1. Define each of the five predicables. 

2. In what sense may we say that the genus is part of the 

species, and in what sense that the species is part of the 
genus ? 

3. Select from the terms in the sixth question of Chapter I, 

Section III, p. 287, such as are genera, species, highest 
genera, or lowest species of other terms. 

4. Explain the expressions sui generis, homogeneous, hetero- 

geneous, summum genus, infima species, tree of Porphyry. 

5. Name a property and accident of each of the following 

classes : — Circle, Planet, Bird, Member of Parliament, Ru- 
minant Animal. 

6. What are the rules of correct logical division ? 

7. The first name in each of the following series of terms is that 

of a class which you are to divide and subdivide so as to 
include all the subjoined minor classes in accordance with 
the laws of division. 

(1) People. (2) Triangle. (3) Reasoning. 

Laity Equiangular Induction (Imperfect) 

Aliens Isosceles Deduction 

Naturalized Subjects Right angled Mediate Inference 



METHOD. 



311 



(1) People. (2) Triangle. 

Peers Scalene 

Natural-born Subjects Obtuse-angled 
Clergy 
Baronets 
Commons 



(3) Reasoning. 
Induction 

Hypothetical Syllogism 
Disjunctive Syllogism 



8. Divide any of the following classes : — Governments, Sciences, 

Logical terms, Propositions. 

9. Of what does a logical definition consist ? 

10. What are the rules of correct definition ? 

11. What rules do the following definitions break ? 

(1) Life is the sum of the vital functions. 

(2) Genus is the material part of the species. 

(3) Illative conversion is that in which the truth of the con- 

verse can be inferred from that of the convertend. 

(4) Mineral substances are those which have not been pro- 

duced by the powers of vegetable or animal life. 

(5) An equilateral triangle is a triangle whose sides and angles 

are respectively equal. 

(6) An acute- angled triangle is one which has an acute angle. 

12. Define classification, and give the derivation of the word. 

13. What do you mean by important characters in classification? 

14. State the requisites of a good classification. 

15. What are the three purposes for which we use language ? 

16. What are the essentials of language as an instrument ot 

scientific record ? 



SECTION III. 
COMPLETE METHOD. 



1. Define Empirical Law, and find a few additional instances of 

such laws. 

2. What are the three steps of the Complete Method ? 

3. Trace some of the successive steps in the progress of the 



312 EXERCISES ASTD QUESTIONS. 

theory of gravitation, showing that it was established by 
this method. 

4. What do you mean by the explanation of a fact ? 

5. State the three ways in which a law of nature may be ex- 

plained, and suggest some additional instances of each case. 

6. State the five rules of method given in the Port Royal Logic. 

7. Explain Descartes' rules for the attainment of truth. 



CHAPTER YII- 
RECENT LOGICAL VIEWS. 



SECTION I. 

THE QUANTIFICATION OF THE PREDICATE. 

What does the quantification of the predicate mean ? 
Assign to each of the following propositions its proper sym- 
bol, and the symbol of its converse : 

(1) Knowledge is power. 

(2) Some rectangles are all squares. 

(3) Only the honest ultimately prosper. 

(4) Princes have but their titles for their glories. 

(5) In man there is nothing great but mind. 

(6) The end of philosophy is the detection of unity. 

Draw all the contrapositive propositions and immediate infer- 
ences you can from the following propositions : — 

(1) London is a great city. 

(2) London is the capital of England. 

(3) All ruminant animals are all cloven-footed animals. 

(4) Some members of parliament are all the ministers. 
Write out in Hamilton's notation the moods Baroko, Darapti, 

Felapton, Bokardo. 



RECEtfT LOGICAL VIEWS. 313 

SECTION II. 
BOOLE'S SYSTEM OF LOGIC. 

1. Apply this system of inference to prove the syllogisms on 

p. 130, in Cesare, and Camestres. 

2. Show that if all A'a are not B'b, then no B'b are A'a ; and 

that if all A'a are all B'a, then all not ^4's are all not B'a. 

3. Develop the term substance, as regards the terms vegetable, 

animal, organic ; then select the combinations which agree 
with these premises : 

" What is vegetable is not animal but is organic; what 
is animal is organic." 

4. Test the validity of this argument : " Good always triumphs, 

and vice always fails ; therefore the victor cannot be wrong, 
nor the vanquished right.' 

5. It is known of a certain class of things that — 

(1) Where the quality A is, B is not. 

(2) Where B is, and only where B is, G and D are. 

What can we infer from these premises of the class of 
things in which A is not present but C is present ? 

6. If all A'a are B'a ; all B's are O's ; all C's are B'a; show that 

all A'a are B'a, and that all not B'a are not A'a. 




NDEX 

AND GLOSSARY. 

Note. — In this Index and Glossary, besides references to all 
the important topics treated of in the volume, may be found brief 
definitions of all the logical and philosophical terms employed, 
and short sketches of the lives of the principal writers men- 
tioned. 



Abacus, the logical, 285. 

Abscissio Infiniti (the cutting 
off of the infinite or negative 
part), the process by which 
we determine the position of 
an object in a system of 
classes, by successive com- 
parison and rejection of those 
classes to which it does not 
belong. 

Absolute terms, i.e., non-rela- 
tive terms, 27 ; sometimes 
used as name of non-conno- 
tative terms, 45. 

Abstract terms, 22, 45. 

Accent, fallacy of, 167. 

Accident, fallacy of, 169 ; the 
predicable, 232. 

Accidental definition is a defi- 
nition which assigns the pro- 
perties of a species, or the 



accidents of an individual ; it 

is more commonly called a 

Description. 
Added determinants, inference 

by, 91. 
Adequate knowledge, 59. 
A dicto secundum quid, etc., 

fallacy of, 169. 
Adjectives, 23. 
Adverbials, 99. 
Affirmative propositions, 67. 
Algebraic reasoning, 61, 190. 
Ambiguity of all, 22 ; of some, 

84 ; of many old terms, 34. 
Ambiguous middle term, 118, 

163. 
Amphibology, fellacy of, 164. 
Ampliative propositions, 73. 
Analogue, a thing analogous 

to some other thing. 
Analysis, method of, 199. 



INDEX AND GLOSSARY. 



315 



Analogy, the cause of ambi- 
guity, 38 ; reasoning by, 167, 
168. 

Analytics (rd 'kvalvTina), the 
title given in the second cen- 
tury to portions of the Orga- 
non, or Logical Treatises of 
Aristotle ; they were distin- 
guished as the Prior and Pos- 
terior Analytics. 

Analytic syllogism, a syllo- 
gism in which the conclusion 
is placed first, the premises 
following as the reasons. See 
Synthetic Syllogism ; the dis- 
tinction is unimportant. 

Antecedent, of a hypothetical 
proposition, 150 ; of an event, 
214. 

Anticipation of nature, 202. 

Antinomy (dvrl, against ; vo/ucs, 
law), the opposition of one 
law or rule to another. Kant. 

A posteriori knowledge, 200. 

A priori knowledge, 200. 

Arbor Porphyriana, see Tree 
of Porphyry. 

Argument, (Latin, argus, from 
apydf, clear, manifest,) the 
process of reasoning, the 
showiDg or proving that 
which is doubtful by that 
which is known. See Infer- 
ence. The middle term of a 
syllogism is sometimes called 
specially the argument. 

Argumentum a fortiori, an 
argument in which we prove 



that the case in question is 
more strong or probable than 
one already conceded to be 
sufficiently so. 

Argumentum ad hominem, 
172. 

Argumentum ad judicium, an 
appeal to the common sense 
of mankind. 

Argumentum ad ignorantiam, 
an argument founded on the 
ignorance of adversaries. 

Argumentum ad populum, 172. 

Argumentum ad verecundiam, 
an appeal to our respect for 
some great authority. 

Argumentum ex concesso, a 
proof derived from a proposi- 
tion already conceded. 

Aristotle, one of the greatest 
philosophers of antiquity (b.c. 
384-322), a pupil of Plato, and 
preceptor of Alexander the 
Great. Aristotle wrote fam- 
ous works on Metaphysics, 
Physics, Logic and Psychol- 
ogy. His Logic has furnished 
the foundations of the science 
treated under that name since 
his day, and he may justly be 
regarded as the father of that 
science. His doctrines were 
accepted by the schoolmen of 
the European Universities 
and, though strangely mis- 
understood by them, were re- 
garded as having an almost 
divine authority. 



316 



INDEX AND GLOSSARY. 



Aristotle's Dicta, 111. 

Assertion, (ad, to ; sero, to 
join,) a statement or proposi- 
tion, affirmative or negative. 

Association of ideas, (associo, 
to accompany ; socius, a com- 
panion,) the natural connec- 
tion existing in the mind be- 
tween impressions which have 
previously coexisted, or which 
are similar. Any idea tends 
to bring into the mind its 
associated ideas, in accordance 
with the two great laws of 
association, the Law of Con- 
tiguity, and the Law of 
Similarity. 

Assumption, (assumo, to take 
for granted,) any proposition 
taken as the basis of argu- 
ment ; in a special sense, the 
minor premise of a categori- 
cal syllogism. 

Attribute, (attribuo, to give or 
ascribe to,) a quality or cir- 
cumstance which may be 
affirmed (or denied) of a 
thing ; opposed to Substance, 
which see. 

Attribute in grammar, 98. 

Attributive term, i.e., Connota- 
tive term, 43. 

Axiom, definition of, 110. 

Baconian method, 251. 
Barbara, Celarent, etc., 134. 
Begging the Question, 173. 
Belief, assent to a proposition, 



admitting of any degree of 
strength, from the slightest 
probability to the fullest cer- 
tainty ; see Probability. 

Bentham, George, new system 
of Logic, 268. 

Boole, George, his system of 
Logic, 272. 

Canons of syllogism, 108, 9 ; 
Hamilton's supreme Canon. 

Canons of Mill's Inductive 
Methods, 215. 

Categorematic words, 19. 

Categorical propositions, 67. 

Categories, the summa genera, 
or most extensive classes into 
which things can be distrib- 
uted; they are ten in num- 
ber, as follows : 

Ovala. Substance ; Tioabv, 
Quantity ; Uolov, Quality ; 
Ilpof tc, Relation; TLotelv, 
Action; Tlaox £LV , Passion, or 
suffering ; Jlov, Place ; Uore, 
Time ; KeloBcu, Position ; 
"E^etv, Habit or condition. 

Everything which can be 
affirmed must come under 
one or other of these highest 
predicates, which were de- 
scribed in the first treatise of 
Aristotle's Organon, called 
the Categories. 

Cause, meaning of, 213. 

Aristotle distinguished four 
kinds of causes for the exist- 
ence of a thing — 1. The Ma- 



INDEX AND GLOSSARY. 



317 



terial Cause, the substance or 
matter composing it ; 2. The 
Formal Cause, the pattern, 
type or design, according to 
which it is shaped; 3. The 
Efficient Cause, the force em- 
ployed in shaping it ; 4. The 
Final Cause, the end, motive 
or purpose of the work. 

Chance, ignorance of the causes 
which are in action ; see 
Probability. 

Character, derivation of the 
word, 48. 

Circulus in definiendo, 239. 

Circulus in probando, 173. 

Clearness of knowledge, 57. 

Cognition, (cognosco, to know,) 
knowledge, or the action of 
mind in acquiring knowledge. 

Colligation of Facts, Dr. Whe- 
well's expression for the men- 
tal union of facts by some 
suitable conception. 

Collective terms, 21. 

Combined or complete method 
of investigation, 249. 

Comparison, {com, together ; 
par, equal or like,) the action 
of mind by which we judge 
whether two objects of 
thought are the same or 
different in certain points. 
See Judgment. 

Compatible terms are those 
which, though distinct, are 
not contradictory, and can 
therefore be affirmed of the 



same subject ; as "large " and 
" heavy ;" " bright-colored " 
and "nauseous." 

Complex conception, infer- 
ence by, 92. 

Complex sentence, 98 ; syllo- 
gism, 141. 

Composition of Causes, the 
principle which is exemplified 
in all cases in which the joint 
effect of several causes is 
identical with the sum of their 
separate effects. J. S. Mill. 

Composition, fallacy of, 165. 

Compound sentence, 94, 95. 

Comprehension of terms, see 
Intension. 

Concept, that which is con- 
ceived, the result of the act 
of conception ; nearly synony- 
mous with general notion, 
idea, thought. 

Conception (con, together ; 
capio, to take). An ambigu- 
ous term, meaning properly 
the action of mind in which 
it takes several things to- 
gether, so as to form a general 
notion ; or, again, in which it 
forms " a mental image of the 
several attributes given in 
any word or combination of 
words." Mansel. 

Conceptualists, 14. 

Concrete terms, 22. 

Conditional propositions, 149. 

Confusion of words, ambiguity 
from, 33. 



318 



INDEX AND GLOSSARY. 



Conjugate words, those which 
come from the same root or 
stock, as known, knowing, 
knowingly, knowledge. 

Connotation of terms, 43 ; 
ought to be exactly fixed, 247. 

Consciousness, the immediate 
knowledge which the mind 
has of its sensations and 
thoughts, and, in general, of 
all its present operations. 
Beid. 

Consectary= Corollary. 

Consequence, the connection 
between antecedent and con- 
sequent ; but often used am- 
biguously for the latter. 

Consequent of a hypothetical 
proposition, 150. 

Consequent or effect of a cause, 
214. 

Consequent, fallacy of the, 175. 

Consilience of inductions, the 
agreement of inductions de- 
rived from different and inde- 
pendent series of facts, as 
when we learn the motion of 
the earth by entirely different 
modes of observation and 
reasoning. Whewell. 

Consistency of propositions, 
83. 

Consistent terms, see compat- 
ible terms. 

Contingent, (contingo, to touch,) 
that which may or may not 
happen ; opposed to the neces- 
sary and impossible. 



Contingent matter, 85. 

Continuity, Law of, the prin- 
ciple that nothing can pass 
from one extreme to another 
without passing through all 
the intermediate degrees ; 
motion, for instance, cannot 
be instantaneously produced 
or destroyed. 

Contradiction, Law of, 105. 

Contradictory terms, 26 ; prop- 
ositions, 83. 

Contraposition, conversion by, 
89. 

Converse fallacy of accident, 
169. 

Conversion of propositions, 
86 ; with quantified predicate, 
266. 

Convertend, 87. 

Co-ordinate propositions, 96. 

Copula, 65. 

Corollary, a proposition which 
follows immediately from an- 
other which has been proved. 

Correlative terms, 27. 

Criterion (Kptrr/piov, from Kpivu, 
to judge), any fact, rule, 
knowledge, or means requi- 
site to the formation of a 
judgment which shall decide 
a doubtful question. 

Cross division, 235. 

Data, (plural of datum, that 
which is given,) the facts or 
assertions from which an in- 
ference is to be drawn. 



INDEX AND GLOSSARY. 



319 



Deduction and Induction, 178. 

Deductive method, 227. 

De facto, what actually or 
really happens; opposed to 
dejure, what ought to happen 
by law or right. 

Definition, the logical process, 
238 ; of logic, 1. 

Degree, terms expressing, 26 ; 
questions of, 107. 

Demonstration, (demonstro, to 
point out,) strictly the point- 
ing out the connection be- 
tween premises and conclu- 
sion. The term is more 
generally used for any argu- 
ment or reasoning regarded 
as proving an asserted con- 
clusion. A demonstration is 
either Direct or Indirect. In 
the latter case we prove the 
conclusion by disproving its 
contradictory, or showing 
that the conclusion cannot be 
supposed untrue. 

Demonstrative Induction, 182. 

Descartes, Rene, a French 
philosopher and mathema- 
tician of the most distin- 
guished originality (1596- 
1650) ; author of La Dis- 
cours de la Method, Les Prin- 
cipes, Les Meditations, and 
other works. Descartes has 
been called "the Father of 
Modern Psychology." His 
criterion of truth was the 
clearness of ideas. His first 



principle of knowledge, which 
he declared was left certain 
when everything else was 
denied, is expressed in his 
now famous maxim : Cogito, 
ergo sum. Descartes' method 
was largely suggested by 
mathematical method. He 
believed that the mind ought 
to be studied by the examina- 
tion of consciousness, or by 
what has now come to be 
known as the introspective 
method. 

Descartes on Method, 261. 

De Morgan's logical discov- 
eries and writings, 271. 

Denotation of terms, 41. 

Depth of a notion, see Inten- 
sion. 

Derivatives from the root spec, 
sight, 55. 

Description, see Accidental 



Destructive dilemma, 159. 

Desynonymization of terms, 
51. 

Determination, the distin- 
guishing of parts of a genus 
by reunion of the genus and 
difference. See Division. 

Development of a term, 274. 

Diagrams, of sentences, 99, 
103 ; of syllogisms, 120, 121 ; 
of propositions, 83. 

Dialectic (6ia'?iEx TiK V tekvtj„ the 
art of discourse, from diaXe- 
■yeodcu, to discourse). The 



320 



INDEX AND GLOSSARY. 



original name of Logic, per- 
haps invented by Plato ; also 
used to denote the Logic of 
Probable Matter (Aristotle), 
the right use of Reason and 
Language, the Science of Be- 
ing ; it is thus a highly am- 
biguous term. 

Dichotomy, division by, 107, 
236. 

Dicta de omni et nullo, 111. 

Difference, the practicable, 228. 

Differentiation of terms, 51. 

Dilemma, 158. 

Disbelief, the state of mind in 
which we are fully persuaded 
that some opinion is not true. 
J. S. Mill. It is equivalent 
to belief in the contradictory 
opinion or assertion, and is 
not to be confused with 
Doubt, which see. 

Discourse, or reasoning, 15. 

Discovery, method of, 199. 

Disjunctive, propositions, 150 ; 
syllogism, 156. 

Distinct knowledge, 55. 

Distribution of terms, 79. 

Division, logical, 234; meta- 
physical, 238 ; fallacy of, 
166. 

Doubt, (dubito, to go two 
ways,) the state of mind in 
which we hesitate between 
two or more inconsistent 
opinions. See Disbelief. 

Drift of a proposition, the vary- 
ing meaning which may be 



attributed to the same sen- 
tence according to accentua- 
tion. See Fallacy of accent, 
167. 
Empiricism (efiTrecpia, experi- 
ence), the doctrine of those 
who consider that all knowl- 
edge is derived merely from 
experience. 

Empirical Law, 249. 

Enthymeme, 142. 

Epicheirema, 145. 

Episyllogism, 144. 

Equivocal terms, 31. 

Equivocation, causes of, 33 ; 
fallacy of, 163. 

Essence, (essentia, from esse, to 
be,) " the very being of any- 
thing, whereby it is what it 
is." Locke. It is an ancient 
scholastic word, which cannot 
be really defined, and should 
be banished from use. 

Essential propositions, 72. 

Euler's diagrams, 120, 121. 

Evidence, (e, and videre, to 
see,) literally the seeing of 
anything. The word now 
means any facts apprehended 
by the mind and made the 
grounds of knowledge and 
belief. 

Examples, use of, 175. 

Exceptive propositions, 72. 

Excluded middle, law of, 
166. 

Exclusive propositions, 72. 

Exhaustive division, 107, 236. 



INDEX AND GLOSSARY. 



321 



Experimentum crucis, an ex- 
periment which decides be- 
tween two rival theories, and 
shows which is to be adopted, 
as a finger-post shows which 
of two roads is to be taken. 

Explanation, of facts, 255 ; of 
laws, 256. 

Explicative propositions, 72. 

Exposita, a proposition given 
to be treated by some logical 
process. 

Extension and intension, 39. 

Extensive Syllogism, 149. 

Extremes of a proposition, are 
its ends or terms, the subject 
and predicate. 

Fact, 212. 

Fallacy, purely logical, 162 ; 
semi-logical, 162 ; material, 
169 ; in hypothetical syllo- 
gism, 155 ; in dilemma, 158. 

False cause, fallacy of, 175. 

False propositions, 74. 

Figure of speech, fallacy of, 
168. 

Figures of the syllogism, 127 ; 
their uses, 130. 

Form and matter of thought, 
5. 

Fundamentum divisionis, 234. 

Fundamentum relationis, the 
ground of relation, i.e., the 
series of events or circum- 
stances which establish a re- 
lation between two correlative 
terms. 



Fundamental principles of syl- 
logism, 108. 

Galenian, or fourth figure of 

the syllogism, 131. 
General notions, 14 ; terms, 

20. 
Generalization of names, 47. 
Generic property, 232. 
Genus, 228 ; generalissimum, 

230. 
Geometiical reasoning, 61, 

187 ; Pascal on, 258. 
Grammatical predicate, 98 ; 

sentence, 68. 
Gravitation, theory of, 252. 

Hamilton, Sir William, a 
Scotch philosopher (1788- 
1856); professor at the Uni- 
versity of Edinburgh (1836- 
1856) ; author of Discussions 
in Philosophy and Literature, 
largely reprinted from his 
essays in the Edinburgh Re- 
view, Lectures on Metaphysics, 
and Lectures on Logic. Hamil- 
ton was the most erudite 
philosopher of his time in 
Great Britain. 

Hamilton, Sir W., Method of 
Notation, 268. 

Heterogeneous, 230 ; intermix- 
ture of effects, 224. 

Homogeneous, 268 ; intermix- 
ture of effects, 224. 

Homologue,"jWhatever is homol- 
ogous. 



322 



INDEX AND GLOSSAItY. 



Homology, a special term for 
the analogy existing between 
parts of different plants and 
animals, as between the wing 
of a bird and the lore leg of a 
quadruped, or between the 
scales of a fish and the 
feathers of a bird. 

Homonymous terms, 32. 

Hypothesis, 208. 

Hypothetical propositions, 66 ; 
syllogism, 15. 

Idea (ic)sa, eidog, image), a term 
used ambiguously, but gener- 
ally equivalent to thought, 
notion, concept. Defiued by 
Locke as " Phantasm, notion, 
species, or whatever it is 
which the mind can be em- 
ployed about in thinking." 
To have an idea of a thing is 
to think of that thing. 

Identity, law of, 104. 

Idol (eid(o'Aoi>, eldoc, image), 
Bacon's figurative name for 
the sources of error ; he enu- 
merated four kinds ; Idols of 
the Tribe, which affect all 
people ; Idols of the Cave, 
which are peculiar to an in- 
dividual ; of the Forum, 
which arise in the intercourse 
of men ; of the Theatre, 
which proceed from the sys- 
tems of philosophers. 

Ignoratio Elenchi, 172. 

Illation (illatum, past participle 



of infero, to bring in). See 
Inference. 

Illative, that which can be in- 
ferred. 

Illicit process, of the minor 
term, 119 ; of the major term, 
128. 

Immediate inference, 86. 

Imperfect figures of the syllo- 
gism, 145. 

Imperfect Induction, 181. 

Impossible matter, 85. 

Inconsistent terms imply qual- 
ities which cannot coexist in 
the same thing. See compat- 
ible terms. 

Inconsistent propositions, 83. 

Indefinite propositions, 68. 

Indefinite or infinite term, is 
a negative term which only 
marks an object by exclusion 
from a class. 

Indesignate propositions. See 
Indefinite propositions. 

Indirect demonstration. See 
Demonstration. 

Indirect inference, method of, 
138. 

Indirect reduction of the syl- 
logism, 137. 

Individual, what cannot be 
divided without losing its 
name and distinctive quali- 
ties, although generally capa- 
ble of physical division or 
partition, which see. 

Induction, 178. 

Inductive syllogism, 183, 184. 



INDEX AND GLOSSARY. 



323 



Inference, defined, 86; imme- 
diate, 87 ; mediate, 113. 

Infima species, 230. 

Innate ideas, see a 'priori 
truths. 

Inseparable accident, 232. 

Intension and extension of 
terms, 39 ; law of relation, 
42. 

Intensive syllogism, 149. 

Intention, first and second, a 
distinction between terms 
thus defined by Hobbes : " Of 
the first intention are the 
names of things, a man, 
stone, &c. ; of the second 
are the names of names, and 
speeches, as universal, par- 
ticular, genus, species, syllo- 
gism, and the like." A term 
of the second intention ex- 
presses the mode in which 
the mind regards or classi- 
fies those of the first inten- 
tion. 

Intermediate link, explanation 
by, 256. 

Intuitive knowledge, 57. 

Irrelevant conclusion, fallacy 
of, 171. 

Judgment, 13. 

Language, the subject of logic, 

10. 
Language, three purposes of, 

245. 
Laws of thought, 2, 104. 



Leibnitz (1646-1716), the great- 
est of the earlier German 
philosophers and celebrated 
as a mathematician and uni- 
versal genius ; author of 
Nouveaux Essais sur V En- 
tendement Humain, and La 
Theodicee Leibnitz invented 
the infinitesimal calculus at 
the same time as Newton. 
Although he advocated some 
strange doctrines, Leibnitz 
must be regarded as one of 
the greatest intellects which 
the world has known. He 
criticised the foundations of 
human knowledge as they 
were set forth by Locke, and 
maintained that there is an- 
other source of knowledge 
than experience, the intui- 
tions of the mind. 

Leibnitz on knowledge, 56. 

Lemma (Xaju.f3dv(D, to take or 
assume), a proposition, a pre- 
mise granted ; in geometry, 
a preliminary proposition. 

Limitation, conversion by, 87. 

Locke, John, an English phy- 
sician and philosopher (1632- 
1704); influential also as a 
writer on government and 
religious toleration ; author of 
the celebrated work Essay 
Concerning Human Under- 
standing, an epoch-making 
production in which human 
knowledge is referred entirely 



324 



INDEX AND GLOSSARY. 



to experience, to the exclu- 
sion of any innate element. 
Locke may justly be regarded 
as the founder of the Eng- 
lish school of psychology. 
His influence in France was 
also great. In Germany 
Locke was less followed and 
has been severely reviewed 
by Leibnitz and others. It is 
likely that he did not see all 
the ultimate bearings of his 
doctrines. He advocated the 
doctrine of representative 
ideas, which prepared the 
way for the doctrines of 
Hume and of Berkeley, and 
has been ably reviewed by 
Thomas Reid and Sir W. 
Hamilton. 

Logic, derivation of name, 1. 

Logical abacus, slate and ma- 
chine, 280. 

Logomachy, a war of words. 

Lowest species, 230. 

Machine, the logical, 280. 

Major, term, 116 ; premise, 
116. 

Many questions, fallacy of, 
176. 

Material fallacies, 169. 

Mathematical induction, 187. 

Matter of thought, 5 ; of pro- 
positions, 85. 

Matter is denned by J. S. Mill 
as "the external cause to 
which we ascribe our sensa- 



tions," or as Permanent Pos- 
sibility of Sensation. 

Mediate inference, 113. 

Membra dividentia, the parts 
into which a class is divided ; 
the constituent species of a 
genus. 

Metaphor, 52. 

Metaphysical division, 238. 

Metaphysics (rd perd rd $voi- 
K'l), the works of Aristotle 
which followed or were 
studied after his Physics. 
First Philosophy, or the so- 
called science of things in 
their own nature ; ontology 
or the science of Being. 

Method ((ledodor;, /uera and 666g, 
way), mode, way or instru- 
ment of accomplishing an 
end. 

Method, 201 ; Pascal on, 257 ; 
Descartes' Discourse on, 263. 

Methods of Induction, Agree- 
ment, 215; Difference, 216; 
of Experiment, 218 ; Joint 
Method, 219 ; Residues, 224 ; 
Concomitant Variations, 221. 

Metonymy (iietu, and ovo/ua, 
name), grammatical name for 
the transfer of meaning of a 
word to a closely connected 
thing, as when we speak of 
the church, meaning the 
people in it. See Transfer 
of meaning. 

Middle Term, 114. 

Mill, John Stuart, an English 



INDEX AND GLOSSARY. 



325 



philosopher and economist 
(1806-1873) ; son of James 
Mill, whose doctrines with 
some modifications he taught; 
author of A System of Logic, 
(in which the syllogism is 
severely criticised and much 
is made of induction,) numer- 
ous political and sociological 
works, and An Examination 
of the Philosophy of Sir W. 
Hamilton. Mill was an em- 
piricist in philosophy and a 
utilitarian in morals. His 
writings have been severely 
criticised by Professor Jevons 
in a series of articles in the 
Contemporary and other re- 
views. 

Mill, J. S., on Connotative 
terms, 43 ; on Induction, 182, 
215 ; on Observation, 206. 

Minor term, 116 ; premise, 118. 

Mnemonic verses, Barbara, 
etc., 133. 

Modal proposition, 73. 

Modus, ponens, 151 ; tollens, 
151. 

Modus, ponendo tollens, 156 ; 
tollendo ponens, 157. 

Moods of the syllogism, 124; 
according to Hamilton, 268. 

Muller, F. Max, a German 
philologist of note (born in 
1823), still (1883) and for a 
long time a resident in Eng- 
land and professor at Ox- 
ford University. Professor 



Muller is a fascinating and 
informing writer, but his 
theories of language have 
been severely criticised by 
Professor W. D. Whitney, 
an American philologist and 
professor in Yale College. 

Name, or term, 17. 

Necessary matter, 85. 

Necessity (ne, not; and cesso, 
to cease), that which always 
is and cannot but be. 

Negation, conversion by, 88. 

Negative, terms, 24; proposi- 
tions, 24; premises, fallacy 
of, 102. 

Newton's experiments, 252. 

Nominal definitions, 259. 

Nominalists, 14. 

Non causa, pro causa, 175. 

Non sequitur, 175. 

Notion (nosco, to know), the 
action of apprehending or 
taking note of the various 
qualities of an object ; or 
more commonly the result of 
that action. See Idea, Con- 
cept. 

Notiora naturae, 199. 

Novum Organum, first apho- 
risms of, 202. 

Numerically definite syllogism, 
184. 

Object of verb, 98. 
Objective, that which belongs 
to the object of thought, the 



326 



INDEX AND GLOSSARY. 



non-ego ; opposed to 

jectice, wliicli see. 

Obscure knowledge, 57. 

Observation, 206. 

Occasion of an event, the proxi- 
mate cause, or last condition 
wliicli is requisite to bring 
other causes into action, 213. 

Opposite terms, 24. 

Opposition of propositions, 83. 

Organon (bpyavov, Latin Or- 
ganum, Instrument), a name 
for Aristotle's logical trea- 
tises, first generally used in 
the 15th century, implying 
that they may be regarded as 
an instrument to assist the 
mind. The name was adopted 
by Bacon for his Novum Or- 
ganum. 

Paradox (napa, 66%a, contrary to 
opinion), an assertion con- 
trary to common opinion, and 
which may or may not prove 
true ; often wrongly used to 
mean what is self-contradic- 
tory and absurd. 

Paralogism {napakoyi(,oiiai, to 
reason wrongly), a purely 
logical fallacy, or breach of 
the rules of deductive logic. 

Parity of reasoning, an expres- 
sion used to denote that when 
one case has been demon- 
strated, other similar cases 
can be demonstrated by a like 
course of reasoning. 



Paronymous words, see Conju- 
gate words. 

Particular propositions, 67. 

Particular premises, fallacy 
of, 162. 

Partition or physical divi- 
sion, 238. 

Pascal, Blaise, a French thinker 
of wonderful genius and not 
less distinguished piety (1623- 
1662), who excelled in geom- 
etry and other branches of 
mathematics ; author of the 
famous Provincial Letters, in 
which he powerfully de- 
nounces the Jesuits, and the 
still more celebrated Thoughts, 
designed to humble the rea- 
son of man in the presence 
of the great mysteries of be- 
ing and lead to a devout 
Christian faith. His works 
are characterized by remark- 
able insight, dialectic skill 
and eloquence. 

Per accidens, conversion, 87. 

Perfect Figure of the Syllo- 
gism, 134. 

Perfect knowledge, characters 
of, 56. 

Periodic changes, 223. 

Peripatetic Philosophy (7repi- 
Trario), to walk about), the 
name usually given to the 
doctrines of Aristotle and his 
followers, who are said to 
have carried on their studies 
and discussions while walking 



INDEX AND GLOSSARY. 



$21 



about the halls and prome- 
nades of the Lyceum. 

Petitio Principii, 173. 

Phenomenon, 213. 

Physical definition assigns the 
parts into which a thing may 
be separated by partition or 
physical division. 

Polylemma, an argument of 
the same form as a dilemma, 
but in which there are more 
than two alternatives. 

Porphyry, tree of, 232. 

Port Royal Logic, 259. 

Positive terms, 24. 

Post hoc, ergo propter hoc, 
175. 

Postulate (postulatum, a thing 
demanded), a proposition 
which is necessarily demanded 
as a basis of argument ; in 
geometry, the postulates de- 
fine the practical conditions 
required. 

Predicables, 227. 

Predicaments ( prmdicamenta, 
what can be predicated), see 
Categories. 

Predicate, 66, 80, 98, 263. 

Premise, or Premiss, 113. 

Primary Laws of Thought, 104, 

Principle (principium, begin- 
ning), the first source of any- 
thing ; sometimes specially 
used to mean the major 
premise of a syllogism. 

Privative conception, infer- 
ence by, 91. 



Privative terms, 26. 

Probability, quantity or de- 
gree of belief, or more truly, 
quantity of information con- 
cerning an uncertain event, 
measured by the ratio of the 
number of cases favorable to 
the event to the total number 
of cases which are possible. 

Probability, of propositions, 
74; of inductions, 181. 

Problem (rcpo^y/ua, that which 
is thrown down), an assertion 
put forward for proof or dis- 
proof. 

Proof, the assigning a reason 
or argument for the support 
of a given proposition. 

Proper names, 29, 32, 44. 

Propositions, see the chap- 
ter on, pp. 64, 99, and the 
particular references in this 
Index. 

Prosyllogism, 144. 

Proximate genns, 237. 

Quantification of predicate, 

263 
Quantity of propositions, 67 ; 

questions of quantity, 68. 
Quaternio terminorum, 162. 

Ramean tree, see Tree of Por- 



Ratiocination, a name equiva- 
let to Syllogism or Deduc- 
tion, adopted by J. S. Mill. 

Realism, 14. 



328 



INDEX AND GLOSSARY. 



Reason {ratio from reor, to 
think), a term of wide and 
ambiguous meaning ; it has 
sometimes been specially used 
to denote the minor premise 
of a syllogism. 

Reasoning, or discourse, 15. 

Record, language as instru- 
ment of, 245. 

Reductio ad absurdum or ad 
impombile, an indirect dem- 
onstration founded upon the 
impossibility of a contradic- 
tory supposition. 

Reduction of the syllogistic 
figures, 135 ; of hypothetical 
to categorical syllogisms, 153. 

Relation (relatum, past parti- 
ciple of refero, to bear back), 
any connection in thought or 
fact between two things. 

Relative terms, 27. 

Residual phenomena, 226. 

Residues, method of, 225. 

Rules of the syllogism, 113. 

Scholastic Philosophy, a gen- 
eral name for the systems of 
philosophy taught during the 
middle ages from the 9th to 
the 16th century, flourishing 
chiefly in the 13th and 14th 
centuries. The subject was 
chiefly the logic of Aristotle, 
varied with theology, meta- 
physics, grammar, or rhetoric. 

Second Intention, see Inten- 
tion. 



Secundi adjacentis, of the 
second adjacent, an expres- 
sion in incorrect Latin, ap- 
plied to a grammatical sen- 
tence or proposition contain- 
ing only two parts, the sub- 
ject and verb, without a dis- 
tinct copula. 

Self-contradictory terms, 26. 

Semilogical fallacies, 162. 

Sentence, grammatical, 65. 

Separable accident, 232. 

Significates of a term are 
things denoted or signified by 
it. 

Similars, substitution of, 282. 

Simple, apprehension, 12 ; con- 
version, 88, 266. 

Singular, terms, 20 ; proposi- 
tions, 69. 

Sophism (o6(f>LOfia, from ootyia, 
wisdom), a false argument ; 
the name often implies that a 
false argument is consciously 
used for deception. 

Sorites, 145. 

Specialization of names, 50. 

Species, in logic, 228 ; in 
natural history, 231. 

Spencer, Herbert, a contempo- 
rary English thinker and 
writer of great ability and 
influence (1820); author of 
. many miscellaneous works, 
but most celebrated as the 
writer of the Synthetic Phil- 
osophy, an undertaking of 
great magnitude not yet 



INDEX AND GLOSSARY. 



329 



(1883) completed. Spencer 
has covered nearly the whole 
range of speculative thought, 
and his aim is to apply the 
doctrine of evolution to every 
department of knowledge. 
He is a clear and instructive, 
but sometimes a misleading, 
writer, as any one is likely to 
be who undertakes to culti- 
vate so wide a field in the 
service of a theory already 
formed rather than derived 
from a minute study of the 
facts in the different depart- 
ments of knowledge. 

Subaltern, propositions, 82 ; 
genera and species, 233. 

Subalternans, subalternates, 
82. 

Subcontrary Propositions, 82. 

Subject of a proposition, 66. 

Subjective, that which belongs 
to the thinking subject, the 
ego, or mind engaged in 
thought ; opposed to objective, 
which see. 

Subordinate propositions, 97. 

Substance {sub, under ; stans 
from stare, to stand), that 
which underlies and bears 
phenomena or attributes ; 
strictly speaking it is either 
mind or matter, but it is 
more commonly used in the 
material sense. 

Substitution of similars, see 
similars. 



Subsumption {sub, under; sumo, 
to take or put), a name used 
by Sir W. Hamilton for the 
minor premise of a syllo- 
gism, because it brings or 
subsumes a special case under 
the rule expressed in the 
major premise or sumption. 

Subsumption of a law is Mr. 
Mill's expression for the third 
mode of explaining a law by 
showing it to be a particu- 
lar case of a more general 
law. 

Sufficient Reason, Principle or 
Law of, 112. 

Sui generis, 230. 

Summum genus, 230. 

Sumption {sumo, to take), Sir 
W. Hamilton's name for the 
major premise of a syllo- 
gism. 

Syllogism, 10, 113 ; inductive, 
178. 

Symbolical knowledge, 60. 

Syncategorematic words, 18. 

Synthesis, 200. 

Synthetic syllogism, a syllo- 
gism in which the conclu- 
sion stands last ; see Analytic 
syllogism. 

System, {ovary/ua, from avvia- 
ttji-u, to put together), a con- 
nected body of knowledge. 

Tacit premise, 142. 
Tautologous propositions, 73. 
Tendency, 213. 



S1 



/ 



330 



INDEX AND GLOSSARY. 






£ 



Terms, see chapter on, pp. 17, 
62. 

Tertii adjacentis, of the third 
adjacent, an expression in in- 
correct Latin, applied to a 
grammatical sentence or prop- 
osition in which the subject, 
copula and predicate, are all 
distinctly stated. 

Theory (Beupia, contemplation), 
knowledge of principles, as 
opposed to practice ; ambigu- 
ously used, see p. 210. 

Thesis {Beoii;, from tWtj/ui, to 
place), an assertion or propo- 
sition which is put forth to be 
proved or supported by argu- 
ments. 

Thoughts or things, the object 
of logic, 11. 

Totum divisum, a class or 
notion which is divided into 
parts by a difference. 

Traduction, 179. 

Transfer of meaning of terms, 
35. 

Tree of Porphyry, 232. 

Trilemma, an argument resem- 
bling a dilemma, but in which 
there are three alternatives. 

Truth, conformity of our 
knowledge with the things 
known. 



Ultra-total distribution, 266. 
Uniformity of nature, 185. 
Universal propositions, 67; 

70 ; affirmative, 68 ; negative, 

67. 
Univocal terms, 31. 

Variations, method of, 221. 
Verb, 94. 

Watts, Isaac, an English 
clergyman, hymn-writer and 
theologian (1674-1748) ; author 
of a useful practical work on 
logic which was very popular 
in its time, but which is now 
little known. 

Weakened conclusion, 129. 

Whately, Richard, Archbishop 
of Dublin, an English eccle- 
siastic and writer on logic, 
political economy and rhetoric 
(1787-1863); a shrewd and 
ingenious writer, but lacking 
in profound erudition as a 
logician. Whately's works 
on logic and rhetoric have 
been until recently very pop- 
ular, especially in America, 
as text-books on these sub- 



jects. 
Worse 
270. 



relation (Hamilton), 



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